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Theorem mpteq2i 4104
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 4103 1 (𝑥𝐴𝐵) = (𝑥𝐴𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1363  wcel 2159  cmpt 4078
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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-ral 2472  df-opab 4079  df-mpt 4080
This theorem is referenced by:  frecsuc  6425  fodjuomni  7164  fodjumkv  7175  axcaucvg  7916  0tonninf  10456  1tonninf  10457  cbvsum  11385  cbvprod  11583  eirraplem  11801  cnmpt12f  14169  fsumcncntop  14439  dvef  14571  nninfsellemqall  15148  nninfomni  15152  exmidsbthr  15155
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