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Theorem mpteq1iOLD 5206
Description: An equality theorem for the maps-to notation. (Contributed by Glauco Siliprandi, 17-Aug-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
mpteq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
mpteq1iOLD (𝑥𝐴𝐶) = (𝑥𝐵𝐶)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵
Allowed substitution hint:   𝐶(𝑥)

Proof of Theorem mpteq1iOLD
StepHypRef Expression
1 mpteq1i.1 . 2 𝐴 = 𝐵
2 mpteq1 5202 . 2 (𝐴 = 𝐵 → (𝑥𝐴𝐶) = (𝑥𝐵𝐶))
31, 2ax-mp 5 1 (𝑥𝐴𝐶) = (𝑥𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cmpt 5192
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-opab 5172  df-mpt 5193
This theorem is referenced by: (None)
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