ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fveq12i Unicode version

Theorem fveq12i 5183
Description: Equality deduction for function value. (Contributed by FL, 27-Jun-2014.)
Hypotheses
Ref Expression
fveq12i.1  |-  F  =  G
fveq12i.2  |-  A  =  B
Assertion
Ref Expression
fveq12i  |-  ( F `
 A )  =  ( G `  B
)

Proof of Theorem fveq12i
StepHypRef Expression
1 fveq12i.1 . . 3  |-  F  =  G
21fveq1i 5179 . 2  |-  ( F `
 A )  =  ( G `  A
)
3 fveq12i.2 . . 3  |-  A  =  B
43fveq2i 5181 . 2  |-  ( G `
 A )  =  ( G `  B
)
52, 4eqtri 2060 1  |-  ( F `
 A )  =  ( G `  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1243   ` cfv 4902
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  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-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator