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Theorem funeqd 5614
Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013.)
Hypothesis
Ref Expression
funeqd.1
Assertion
Ref Expression
funeqd

Proof of Theorem funeqd
StepHypRef Expression
1 funeqd.1 . 2
2 funeq 5612 . 2
31, 2syl 16 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  Funwfun 5587
This theorem is referenced by:  funopg  5625  funsng  5639  f1eq1  5781  fvn0ssdmfun  6022  funcnvuni  6753  shftfn  12906  isstruct2  14641  strle1  14728  monfval  15127  ismon  15128  monpropd  15132  isepi  15135  isfth  15283  lubfun  15610  glbfun  15623  acsficl2d  15806  frlmphl  18812  eengbas  24284  ebtwntg  24285  ecgrtg  24286  elntg  24287  istrl  24539  ispth  24570  isspth  24571  0spth  24573  1pthonlem1  24591  constr2spthlem1  24596  2pthlem1  24597  constr2pth  24603  constr3pthlem2  24656  ajfun  25776  sitgf  28289  fperdvper  31715  dfateq12d  32214  afvres  32257  usgra2pthspth  32351  estrres  32645
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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-fun 5595
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