ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fveq2i Structured version   GIF version

Theorem fveq2i 5102
Description: Equality inference for function value. (Contributed by NM, 28-Jul-1999.)
Hypothesis
Ref Expression
fveq2i.1 A = B
Assertion
Ref Expression
fveq2i (𝐹A) = (𝐹B)

Proof of Theorem fveq2i
StepHypRef Expression
1 fveq2i.1 . 2 A = B
2 fveq2 5099 . 2 (A = B → (𝐹A) = (𝐹B))
31, 2ax-mp 7 1 (𝐹A) = (𝐹B)
Colors of variables: wff set class
Syntax hints:   = wceq 1226  cfv 4825
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-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-rex 2286  df-v 2533  df-un 2895  df-sn 3352  df-pr 3353  df-op 3355  df-uni 3551  df-br 3735  df-iota 4790  df-fv 4833
This theorem is referenced by:  fveq12i  5104  ot1stg  5698  ot2ndg  5699  ot3rdgg  5700  algrflem  5769  tfr2a  5854  rdgi0g  5882  rdg0  5891  frec0g  5898  1prl  6399  1pru  6400  ltexprlemell  6429  ltexprlemelu  6430  recexprlemell  6450  recexprlemelu  6451
  Copyright terms: Public domain W3C validator