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Theorem mpteq2i 3947
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 3946 1 (𝑥𝐴𝐵) = (𝑥𝐴𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1296  wcel 1445  cmpt 3921
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-11 1449  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-ral 2375  df-opab 3922  df-mpt 3923
This theorem is referenced by:  frecsuc  6210  fodjuomni  6892  fodjumkv  6903  axcaucvg  7532  0tonninf  9994  1tonninf  9995  cbvsum  10903  eirraplem  11213  nninfsellemqall  12621  nninfomni  12625  exmidsbthr  12627
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