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Theorem mpteq2dvaOLD 5249
Description: Obsolete version of mpteq2dva 5248 as of 11-Nov-2024. (Contributed by Scott Fenton, 25-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
mpteq2dva.1 ((𝜑𝑥𝐴) → 𝐵 = 𝐶)
Assertion
Ref Expression
mpteq2dvaOLD (𝜑 → (𝑥𝐴𝐵) = (𝑥𝐴𝐶))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝐴(𝑥)   𝐵(𝑥)   𝐶(𝑥)

Proof of Theorem mpteq2dvaOLD
StepHypRef Expression
1 nfv 1917 . 2 𝑥𝜑
2 mpteq2dva.1 . 2 ((𝜑𝑥𝐴) → 𝐵 = 𝐶)
31, 2mpteq2da 5246 1 (𝜑 → (𝑥𝐴𝐵) = (𝑥𝐴𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396   = wceq 1541  wcel 2106  cmpt 5231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-12 2171  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-opab 5211  df-mpt 5232
This theorem is referenced by: (None)
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