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Theorem xpcco 18177
Description: Value of composition in the binary product of categories. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypotheses
Ref Expression
xpccofval.t 𝑇 = (𝐶 ×c 𝐷)
xpccofval.b 𝐵 = (Base‘𝑇)
xpccofval.k 𝐾 = (Hom ‘𝑇)
xpccofval.o1 · = (comp‘𝐶)
xpccofval.o2 = (comp‘𝐷)
xpccofval.o 𝑂 = (comp‘𝑇)
xpcco.x (𝜑𝑋𝐵)
xpcco.y (𝜑𝑌𝐵)
xpcco.z (𝜑𝑍𝐵)
xpcco.f (𝜑𝐹 ∈ (𝑋𝐾𝑌))
xpcco.g (𝜑𝐺 ∈ (𝑌𝐾𝑍))
Assertion
Ref Expression
xpcco (𝜑 → (𝐺(⟨𝑋, 𝑌𝑂𝑍)𝐹) = ⟨((1st𝐺)(⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍))(1st𝐹)), ((2nd𝐺)(⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍))(2nd𝐹))⟩)

Proof of Theorem xpcco
Dummy variables 𝑓 𝑔 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 xpccofval.t . . 3 𝑇 = (𝐶 ×c 𝐷)
2 xpccofval.b . . 3 𝐵 = (Base‘𝑇)
3 xpccofval.k . . 3 𝐾 = (Hom ‘𝑇)
4 xpccofval.o1 . . 3 · = (comp‘𝐶)
5 xpccofval.o2 . . 3 = (comp‘𝐷)
6 xpccofval.o . . 3 𝑂 = (comp‘𝑇)
71, 2, 3, 4, 5, 6xpccofval 18176 . 2 𝑂 = (𝑥 ∈ (𝐵 × 𝐵), 𝑦𝐵 ↦ (𝑔 ∈ ((2nd𝑥)𝐾𝑦), 𝑓 ∈ (𝐾𝑥) ↦ ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩))
8 xpcco.x . . . 4 (𝜑𝑋𝐵)
9 xpcco.y . . . 4 (𝜑𝑌𝐵)
108, 9opelxpd 5717 . . 3 (𝜑 → ⟨𝑋, 𝑌⟩ ∈ (𝐵 × 𝐵))
11 xpcco.z . . . 4 (𝜑𝑍𝐵)
1211adantr 479 . . 3 ((𝜑𝑥 = ⟨𝑋, 𝑌⟩) → 𝑍𝐵)
13 ovex 7452 . . . . 5 ((2nd𝑥)𝐾𝑦) ∈ V
14 fvex 6909 . . . . 5 (𝐾𝑥) ∈ V
1513, 14mpoex 8084 . . . 4 (𝑔 ∈ ((2nd𝑥)𝐾𝑦), 𝑓 ∈ (𝐾𝑥) ↦ ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩) ∈ V
1615a1i 11 . . 3 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (𝑔 ∈ ((2nd𝑥)𝐾𝑦), 𝑓 ∈ (𝐾𝑥) ↦ ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩) ∈ V)
17 xpcco.g . . . . . 6 (𝜑𝐺 ∈ (𝑌𝐾𝑍))
1817adantr 479 . . . . 5 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → 𝐺 ∈ (𝑌𝐾𝑍))
19 simprl 769 . . . . . . . 8 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → 𝑥 = ⟨𝑋, 𝑌⟩)
2019fveq2d 6900 . . . . . . 7 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (2nd𝑥) = (2nd ‘⟨𝑋, 𝑌⟩))
21 op2ndg 8007 . . . . . . . . 9 ((𝑋𝐵𝑌𝐵) → (2nd ‘⟨𝑋, 𝑌⟩) = 𝑌)
228, 9, 21syl2anc 582 . . . . . . . 8 (𝜑 → (2nd ‘⟨𝑋, 𝑌⟩) = 𝑌)
2322adantr 479 . . . . . . 7 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (2nd ‘⟨𝑋, 𝑌⟩) = 𝑌)
2420, 23eqtrd 2765 . . . . . 6 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (2nd𝑥) = 𝑌)
25 simprr 771 . . . . . 6 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → 𝑦 = 𝑍)
2624, 25oveq12d 7437 . . . . 5 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → ((2nd𝑥)𝐾𝑦) = (𝑌𝐾𝑍))
2718, 26eleqtrrd 2828 . . . 4 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → 𝐺 ∈ ((2nd𝑥)𝐾𝑦))
28 xpcco.f . . . . . . 7 (𝜑𝐹 ∈ (𝑋𝐾𝑌))
2928adantr 479 . . . . . 6 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → 𝐹 ∈ (𝑋𝐾𝑌))
3019fveq2d 6900 . . . . . . 7 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (𝐾𝑥) = (𝐾‘⟨𝑋, 𝑌⟩))
31 df-ov 7422 . . . . . . 7 (𝑋𝐾𝑌) = (𝐾‘⟨𝑋, 𝑌⟩)
3230, 31eqtr4di 2783 . . . . . 6 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (𝐾𝑥) = (𝑋𝐾𝑌))
3329, 32eleqtrrd 2828 . . . . 5 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → 𝐹 ∈ (𝐾𝑥))
3433adantr 479 . . . 4 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ 𝑔 = 𝐺) → 𝐹 ∈ (𝐾𝑥))
35 opex 5466 . . . . 5 ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩ ∈ V
3635a1i 11 . . . 4 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩ ∈ V)
3719fveq2d 6900 . . . . . . . . . . 11 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (1st𝑥) = (1st ‘⟨𝑋, 𝑌⟩))
38 op1stg 8006 . . . . . . . . . . . . 13 ((𝑋𝐵𝑌𝐵) → (1st ‘⟨𝑋, 𝑌⟩) = 𝑋)
398, 9, 38syl2anc 582 . . . . . . . . . . . 12 (𝜑 → (1st ‘⟨𝑋, 𝑌⟩) = 𝑋)
4039adantr 479 . . . . . . . . . . 11 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (1st ‘⟨𝑋, 𝑌⟩) = 𝑋)
4137, 40eqtrd 2765 . . . . . . . . . 10 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → (1st𝑥) = 𝑋)
4241adantr 479 . . . . . . . . 9 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (1st𝑥) = 𝑋)
4342fveq2d 6900 . . . . . . . 8 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (1st ‘(1st𝑥)) = (1st𝑋))
4424adantr 479 . . . . . . . . 9 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (2nd𝑥) = 𝑌)
4544fveq2d 6900 . . . . . . . 8 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (1st ‘(2nd𝑥)) = (1st𝑌))
4643, 45opeq12d 4883 . . . . . . 7 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → ⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ = ⟨(1st𝑋), (1st𝑌)⟩)
47 simplrr 776 . . . . . . . 8 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → 𝑦 = 𝑍)
4847fveq2d 6900 . . . . . . 7 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (1st𝑦) = (1st𝑍))
4946, 48oveq12d 7437 . . . . . 6 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦)) = (⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍)))
50 simprl 769 . . . . . . 7 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → 𝑔 = 𝐺)
5150fveq2d 6900 . . . . . 6 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (1st𝑔) = (1st𝐺))
52 simprr 771 . . . . . . 7 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → 𝑓 = 𝐹)
5352fveq2d 6900 . . . . . 6 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (1st𝑓) = (1st𝐹))
5449, 51, 53oveq123d 7440 . . . . 5 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → ((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)) = ((1st𝐺)(⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍))(1st𝐹)))
5542fveq2d 6900 . . . . . . . 8 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (2nd ‘(1st𝑥)) = (2nd𝑋))
5644fveq2d 6900 . . . . . . . 8 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (2nd ‘(2nd𝑥)) = (2nd𝑌))
5755, 56opeq12d 4883 . . . . . . 7 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → ⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ = ⟨(2nd𝑋), (2nd𝑌)⟩)
5847fveq2d 6900 . . . . . . 7 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (2nd𝑦) = (2nd𝑍))
5957, 58oveq12d 7437 . . . . . 6 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦)) = (⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍)))
6050fveq2d 6900 . . . . . 6 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (2nd𝑔) = (2nd𝐺))
6152fveq2d 6900 . . . . . 6 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → (2nd𝑓) = (2nd𝐹))
6259, 60, 61oveq123d 7440 . . . . 5 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓)) = ((2nd𝐺)(⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍))(2nd𝐹)))
6354, 62opeq12d 4883 . . . 4 (((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) ∧ (𝑔 = 𝐺𝑓 = 𝐹)) → ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩ = ⟨((1st𝐺)(⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍))(1st𝐹)), ((2nd𝐺)(⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍))(2nd𝐹))⟩)
6427, 34, 36, 63ovmpodv2 7579 . . 3 ((𝜑 ∧ (𝑥 = ⟨𝑋, 𝑌⟩ ∧ 𝑦 = 𝑍)) → ((⟨𝑋, 𝑌𝑂𝑍) = (𝑔 ∈ ((2nd𝑥)𝐾𝑦), 𝑓 ∈ (𝐾𝑥) ↦ ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩) → (𝐺(⟨𝑋, 𝑌𝑂𝑍)𝐹) = ⟨((1st𝐺)(⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍))(1st𝐹)), ((2nd𝐺)(⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍))(2nd𝐹))⟩))
6510, 12, 16, 64ovmpodv 7578 . 2 (𝜑 → (𝑂 = (𝑥 ∈ (𝐵 × 𝐵), 𝑦𝐵 ↦ (𝑔 ∈ ((2nd𝑥)𝐾𝑦), 𝑓 ∈ (𝐾𝑥) ↦ ⟨((1st𝑔)(⟨(1st ‘(1st𝑥)), (1st ‘(2nd𝑥))⟩ · (1st𝑦))(1st𝑓)), ((2nd𝑔)(⟨(2nd ‘(1st𝑥)), (2nd ‘(2nd𝑥))⟩ (2nd𝑦))(2nd𝑓))⟩)) → (𝐺(⟨𝑋, 𝑌𝑂𝑍)𝐹) = ⟨((1st𝐺)(⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍))(1st𝐹)), ((2nd𝐺)(⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍))(2nd𝐹))⟩))
667, 65mpi 20 1 (𝜑 → (𝐺(⟨𝑋, 𝑌𝑂𝑍)𝐹) = ⟨((1st𝐺)(⟨(1st𝑋), (1st𝑌)⟩ · (1st𝑍))(1st𝐹)), ((2nd𝐺)(⟨(2nd𝑋), (2nd𝑌)⟩ (2nd𝑍))(2nd𝐹))⟩)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394   = wceq 1533  wcel 2098  Vcvv 3461  cop 4636   × cxp 5676  cfv 6549  (class class class)co 7419  cmpo 7421  1st c1st 7992  2nd c2nd 7993  Basecbs 17183  Hom chom 17247  compcco 17248   ×c cxpc 18162
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696  ax-rep 5286  ax-sep 5300  ax-nul 5307  ax-pow 5365  ax-pr 5429  ax-un 7741  ax-cnex 11196  ax-resscn 11197  ax-1cn 11198  ax-icn 11199  ax-addcl 11200  ax-addrcl 11201  ax-mulcl 11202  ax-mulrcl 11203  ax-mulcom 11204  ax-addass 11205  ax-mulass 11206  ax-distr 11207  ax-i2m1 11208  ax-1ne0 11209  ax-1rid 11210  ax-rnegex 11211  ax-rrecex 11212  ax-cnre 11213  ax-pre-lttri 11214  ax-pre-lttrn 11215  ax-pre-ltadd 11216  ax-pre-mulgt0 11217
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-ne 2930  df-nel 3036  df-ral 3051  df-rex 3060  df-reu 3364  df-rab 3419  df-v 3463  df-sbc 3774  df-csb 3890  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-pss 3964  df-nul 4323  df-if 4531  df-pw 4606  df-sn 4631  df-pr 4633  df-tp 4635  df-op 4637  df-uni 4910  df-iun 4999  df-br 5150  df-opab 5212  df-mpt 5233  df-tr 5267  df-id 5576  df-eprel 5582  df-po 5590  df-so 5591  df-fr 5633  df-we 5635  df-xp 5684  df-rel 5685  df-cnv 5686  df-co 5687  df-dm 5688  df-rn 5689  df-res 5690  df-ima 5691  df-pred 6307  df-ord 6374  df-on 6375  df-lim 6376  df-suc 6377  df-iota 6501  df-fun 6551  df-fn 6552  df-f 6553  df-f1 6554  df-fo 6555  df-f1o 6556  df-fv 6557  df-riota 7375  df-ov 7422  df-oprab 7423  df-mpo 7424  df-om 7872  df-1st 7994  df-2nd 7995  df-frecs 8287  df-wrecs 8318  df-recs 8392  df-rdg 8431  df-1o 8487  df-er 8725  df-en 8965  df-dom 8966  df-sdom 8967  df-fin 8968  df-pnf 11282  df-mnf 11283  df-xr 11284  df-ltxr 11285  df-le 11286  df-sub 11478  df-neg 11479  df-nn 12246  df-2 12308  df-3 12309  df-4 12310  df-5 12311  df-6 12312  df-7 12313  df-8 12314  df-9 12315  df-n0 12506  df-z 12592  df-dec 12711  df-uz 12856  df-fz 13520  df-struct 17119  df-slot 17154  df-ndx 17166  df-base 17184  df-hom 17260  df-cco 17261  df-xpc 18166
This theorem is referenced by:  xpcco1st  18178  xpcco2nd  18179  xpcco2  18181  xpccatid  18182
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