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Theorem ifeq12d 3961
 Description: Equality deduction for conditional operator. (Contributed by NM, 24-Mar-2015.)
Hypotheses
Ref Expression
ifeq1d.1
ifeq12d.2
Assertion
Ref Expression
ifeq12d

Proof of Theorem ifeq12d
StepHypRef Expression
1 ifeq1d.1 . . 3
21ifeq1d 3959 . 2
3 ifeq12d.2 . . 3
43ifeq2d 3960 . 2
52, 4eqtrd 2498 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  ifcif 3941 This theorem is referenced by:  ifbieq12d  3968  csbif  3991  oev  7183  dfac12r  8547  xaddpnf1  11454  swrdccat3blem  12720  ruclem1  13964  eucalgval  14211  gsumpropd  15899  gsumpropd2lem  15900  gsumress  15903  mulgfval  16143  mulgpropd  16175  frgpup3lem  16795  subrgmvr  18123  isobs  18751  uvcfval  18815  matsc  18952  scmatscmide  19009  marrepval0  19063  marepvval0  19068  mulmarep1el  19074  madufval  19139  madugsum  19145  minmar1fval  19148  pmat1opsc  19200  pmat1ovscd  19201  mat2pmat1  19233  decpmatid  19271  idpm2idmp  19302  pcoval  21511  pcorevlem  21526  itg2const  22147  ditgeq3  22254  efrlim  23299  lgsval  23575  rpvmasum2  23697  gxfval  25259  gxval  25260  xrhval  27996  itg2addnclem  30066  ftc1anclem5  30094  dgrsub2  31084  dirkerval  31873  fourierdlem111  32000  fourierdlem112  32001  fourierdlem113  32002  hdmap1fval  37524 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-rab 2816  df-v 3111  df-un 3480  df-if 3942
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