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Theorem iuneq12dOLD 5020
Description: Obsolete version of iuneq12d 5021 as of 1-Sep-2025. (Contributed by Drahflow, 22-Oct-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
iuneq1d.1 (𝜑𝐴 = 𝐵)
iuneq12dOLD.2 (𝜑𝐶 = 𝐷)
Assertion
Ref Expression
iuneq12dOLD (𝜑 𝑥𝐴 𝐶 = 𝑥𝐵 𝐷)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵   𝜑,𝑥
Allowed substitution hints:   𝐶(𝑥)   𝐷(𝑥)

Proof of Theorem iuneq12dOLD
StepHypRef Expression
1 iuneq1d.1 . . 3 (𝜑𝐴 = 𝐵)
21iuneq1d 5019 . 2 (𝜑 𝑥𝐴 𝐶 = 𝑥𝐵 𝐶)
3 iuneq12dOLD.2 . . . 4 (𝜑𝐶 = 𝐷)
43adantr 480 . . 3 ((𝜑𝑥𝐵) → 𝐶 = 𝐷)
54iuneq2dv 5016 . 2 (𝜑 𝑥𝐵 𝐶 = 𝑥𝐵 𝐷)
62, 5eqtrd 2777 1 (𝜑 𝑥𝐴 𝐶 = 𝑥𝐵 𝐷)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  wcel 2108   ciun 4991
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-v 3482  df-ss 3968  df-iun 4993
This theorem is referenced by: (None)
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