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Theorem f1eq123d 5816
Description: Equality deduction for one-to-one functions. (Contributed by Mario Carneiro, 27-Jan-2017.)
Hypotheses
Ref Expression
f1eq123d.1
f1eq123d.2
f1eq123d.3
Assertion
Ref Expression
f1eq123d

Proof of Theorem f1eq123d
StepHypRef Expression
1 f1eq123d.1 . . 3
2 f1eq1 5781 . . 3
31, 2syl 16 . 2
4 f1eq123d.2 . . 3
5 f1eq2 5782 . . 3
64, 5syl 16 . 2
7 f1eq123d.3 . . 3
8 f1eq3 5783 . . 3
97, 8syl 16 . 2
103, 6, 93bitrd 279 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  -1-1->wf1 5590
This theorem is referenced by:  fthf1  15286  cofth  15304  istrkgld  23857  istrkg2ld  23858  isushgra  24301  usgraeq12d  24362  usgra0v  24371  usgra1v  24390  usgrares1  24410  2spontn0vne  24887  usgra2pthspth  32351  isushgr  32367  usgedgleord  32419  isfusgra  32424  usgresvm1  32443  usgresvm1ALT  32447
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  df-f1 5598
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