ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fveq12d Structured version   GIF version

Theorem fveq12d 5127
Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008.)
Hypotheses
Ref Expression
fveq12d.1 (φ𝐹 = 𝐺)
fveq12d.2 (φA = B)
Assertion
Ref Expression
fveq12d (φ → (𝐹A) = (𝐺B))

Proof of Theorem fveq12d
StepHypRef Expression
1 fveq12d.1 . . 3 (φ𝐹 = 𝐺)
21fveq1d 5123 . 2 (φ → (𝐹A) = (𝐺A))
3 fveq12d.2 . . 3 (φA = B)
43fveq2d 5125 . 2 (φ → (𝐺A) = (𝐺B))
52, 4eqtrd 2069 1 (φ → (𝐹A) = (𝐺B))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  cfv 4845
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  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-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853
This theorem is referenced by:  nffvd  5130  fvsng  5302  tfrlem3ag  5865  tfrlem3a  5866  tfrlemi1  5887
  Copyright terms: Public domain W3C validator