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Theorem feq1d 4977
Description: Equality deduction for functions. (Contributed by NM, 19-Feb-2008.)
Hypothesis
Ref Expression
feq1d.1  F  G
Assertion
Ref Expression
feq1d  F : -->  G : -->

Proof of Theorem feq1d
StepHypRef Expression
1 feq1d.1 . 2  F  G
2 feq1 4973 . 2  F  G  F : -->  G :
-->
31, 2syl 14 1  F : -->  G : -->
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wceq 1242   -->wf 4841
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-rn 4299  df-fun 4847  df-fn 4848  df-f 4849
This theorem is referenced by:  feq12d  4979  fco2  5000  fssres2  5010  fresin  5011  fmptco  5273  fressnfv  5293  off  5666  caofinvl  5675  f2ndf  5789  eroprf  6135  fseq1p1m1  8726
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