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Theorem feq123d 5726
 Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypotheses
Ref Expression
feq12d.1
feq12d.2
feq123d.3
Assertion
Ref Expression
feq123d

Proof of Theorem feq123d
StepHypRef Expression
1 feq12d.1 . . 3
2 feq12d.2 . . 3
31, 2feq12d 5725 . 2
4 feq123d.3 . . 3
54feq3d 5724 . 2
63, 5bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  -->wf 5589 This theorem is referenced by:  feq123  5727  feq23d  5731  fprg  6080  csbwrdg  12570  evlfcl  15491  yonedalem3a  15543  yonedalem4c  15546  yonedalem3b  15548  yonedainv  15550  iscau  21715  isuhgra  24298  uhgraeq12d  24307  constr3trllem3  24652  isrngo  25380  sseqf  28331  ismfs  28909  isuhgr  32366  uhgeq12g  32370  uhguhgra  32372  uhgrauhg  32373  funcestrcsetclem8  32653  funcsetcestrclem8  32668  funcsetcestrclem9  32669  funcringcsetcOLD2lem8  32851  funcringcsetclem8OLD  32874 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-fun 5595  df-fn 5596  df-f 5597
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