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Theorem mpteq2iaOLD 5270
Description: Obsolete version of mpteq2ia 5269 as of 11-Nov-2024. (Contributed by Mario Carneiro, 16-Dec-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
mpteq2ia.1 (𝑥𝐴𝐵 = 𝐶)
Assertion
Ref Expression
mpteq2iaOLD (𝑥𝐴𝐵) = (𝑥𝐴𝐶)

Proof of Theorem mpteq2iaOLD
StepHypRef Expression
1 eqid 2740 . . 3 𝐴 = 𝐴
21ax-gen 1793 . 2 𝑥 𝐴 = 𝐴
3 mpteq2ia.1 . . 3 (𝑥𝐴𝐵 = 𝐶)
43rgen 3069 . 2 𝑥𝐴 𝐵 = 𝐶
5 mpteq12f 5254 . 2 ((∀𝑥 𝐴 = 𝐴 ∧ ∀𝑥𝐴 𝐵 = 𝐶) → (𝑥𝐴𝐵) = (𝑥𝐴𝐶))
62, 4, 5mp2an 691 1 (𝑥𝐴𝐵) = (𝑥𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1535   = wceq 1537  wcel 2108  wral 3067  cmpt 5249
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-12 2178  ax-ext 2711
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ral 3068  df-opab 5229  df-mpt 5250
This theorem is referenced by: (None)
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