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Theorem mpteq2i 4090
Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)
Hypothesis
Ref Expression
mpteq2i.1 𝐵 = 𝐶
Assertion
Ref Expression
mpteq2i (𝑥𝐴𝐵) = (𝑥𝐴𝐶)

Proof of Theorem mpteq2i
StepHypRef Expression
1 mpteq2i.1 . . 3 𝐵 = 𝐶
21a1i 9 . 2 (𝑥𝐴𝐵 = 𝐶)
32mpteq2ia 4089 1 (𝑥𝐴𝐵) = (𝑥𝐴𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wcel 2148  cmpt 4064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-ral 2460  df-opab 4065  df-mpt 4066
This theorem is referenced by:  frecsuc  6407  fodjuomni  7146  fodjumkv  7157  axcaucvg  7898  0tonninf  10438  1tonninf  10439  cbvsum  11367  cbvprod  11565  eirraplem  11783  cnmpt12f  13756  fsumcncntop  14026  dvef  14158  nninfsellemqall  14734  nninfomni  14738  exmidsbthr  14741
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