ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fneq1i Structured version   GIF version

Theorem fneq1i 4936
Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq1i.1 𝐹 = 𝐺
Assertion
Ref Expression
fneq1i (𝐹 Fn A𝐺 Fn A)

Proof of Theorem fneq1i
StepHypRef Expression
1 fneq1i.1 . 2 𝐹 = 𝐺
2 fneq1 4930 . 2 (𝐹 = 𝐺 → (𝐹 Fn A𝐺 Fn A))
31, 2ax-mp 7 1 (𝐹 Fn A𝐺 Fn A)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1242   Fn wfn 4840
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-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-fun 4847  df-fn 4848
This theorem is referenced by:  fnunsn  4949  fnopabg  4965  f1oun  5089  f1oi  5107  f1osn  5109  ovid  5559  tfri1d  5890  frec2uzrand  8872  frec2uzf1od  8873  frecuzrdgrom  8877  frecfzennn  8884
  Copyright terms: Public domain W3C validator