Theorem colleq1 44371

Description: Equality theorem for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023.)

Assertion

Ref	Expression
colleq1	⊢ (𝐹 = 𝐺 → (𝐹 Coll 𝐴) = (𝐺 Coll 𝐴))

Proof of Theorem colleq1

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝐹 = 𝐺 → 𝐹 = 𝐺)
2		eqidd 2734	. 2 ⊢ (𝐹 = 𝐺 → 𝐴 = 𝐴)
3	1, 2	colleq12d 44370	1 ⊢ (𝐹 = 𝐺 → (𝐹 Coll 𝐴) = (𝐺 Coll 𝐴))

Syntax hints:   → wi 4   = wceq 1541   Coll ccoll 44367

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-ral 3049  df-rex 3058  df-rab 3397  df-v 3439  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4283  df-if 4475  df-sn 4576  df-pr 4578  df-op 4582  df-iun 4943  df-br 5094  df-opab 5156  df-cnv 5627  df-dm 5629  df-rn 5630  df-res 5631  df-ima 5632  df-scott 44353  df-coll 44368

This theorem is referenced by: (None)