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Theorem eqeqan12dOLD 2758
Description: Obsolete version of eqeqan12d 2751 as of 23-Oct-2024. (Contributed by NM, 9-Aug-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 20-Nov-2019.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
eqeqan12dOLD.1 (𝜑𝐴 = 𝐵)
eqeqan12dOLD.2 (𝜓𝐶 = 𝐷)
Assertion
Ref Expression
eqeqan12dOLD ((𝜑𝜓) → (𝐴 = 𝐶𝐵 = 𝐷))

Proof of Theorem eqeqan12dOLD
StepHypRef Expression
1 eqeqan12dOLD.1 . . 3 (𝜑𝐴 = 𝐵)
21adantr 484 . 2 ((𝜑𝜓) → 𝐴 = 𝐵)
3 eqeqan12dOLD.2 . . 3 (𝜓𝐶 = 𝐷)
43adantl 485 . 2 ((𝜑𝜓) → 𝐶 = 𝐷)
52, 4eqeq12dOLD 2757 1 ((𝜑𝜓) → (𝐴 = 𝐶𝐵 = 𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399   = wceq 1543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-cleq 2729
This theorem is referenced by: (None)
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