ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpt2eq3ia Structured version   Unicode version

Theorem mpt2eq3ia 5512
Description: An equality inference for the maps to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)
Hypothesis
Ref Expression
mpt2eq3ia.1  C  D
Assertion
Ref Expression
mpt2eq3ia  ,  |->  C  ,  |->  D

Proof of Theorem mpt2eq3ia
StepHypRef Expression
1 mpt2eq3ia.1 . . . 4  C  D
213adant1 921 . . 3  C  D
32mpt2eq3dva 5511 . 2  ,  |->  C  ,  |->  D
43trud 1251 1  ,  |->  C  ,  |->  D
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1242   wtru 1243   wcel 1390    |-> cmpt2 5457
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-oprab 5459  df-mpt2 5460
This theorem is referenced by:  oprab2co  5781  genpdf  6490  dfioo2  8573
  Copyright terms: Public domain W3C validator