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Theorem mpteq2dfa 45112
Description: Slightly more general equality inference for the maps-to notation. (Contributed by Glauco Siliprandi, 21-Dec-2024.)
Hypotheses
Ref Expression
mpteq2dfa.1 𝑥𝜑
mpteq2dfa.2 ((𝜑𝑥𝐴) → 𝐵 = 𝐶)
Assertion
Ref Expression
mpteq2dfa (𝜑 → (𝑥𝐴𝐵) = (𝑥𝐴𝐶))

Proof of Theorem mpteq2dfa
StepHypRef Expression
1 mpteq2dfa.1 . 2 𝑥𝜑
2 mpteq2dfa.2 . 2 ((𝜑𝑥𝐴) → 𝐵 = 𝐶)
31, 2mpteq2da 5267 1 (𝜑 → (𝑥𝐴𝐵) = (𝑥𝐴𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395   = wceq 1537  wnf 1781  wcel 2103  cmpt 5252
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 2105  ax-9 2113  ax-12 2173  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-opab 5232  df-mpt 5253
This theorem is referenced by: (None)
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