ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpteq2i GIF version

Theorem mpteq2i 3844
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 3843 1 (𝑥𝐴𝐵) = (𝑥𝐴𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1243  wcel 1393  cmpt 3818
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-opab 3819  df-mpt 3820
This theorem is referenced by:  frecsuc  5991  axcaucvg  6972
  Copyright terms: Public domain W3C validator