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Theorem oteq3d 4070
Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
oteq3d  |-  ( ph  -> 
<. C ,  D ,  A >.  =  <. C ,  D ,  B >. )

Proof of Theorem oteq3d
StepHypRef Expression
1 oteq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 oteq3 4067 . 2  |-  ( A  =  B  ->  <. C ,  D ,  A >.  = 
<. C ,  D ,  B >. )
31, 2syl 16 1  |-  ( ph  -> 
<. C ,  D ,  A >.  =  <. C ,  D ,  B >. )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1364   <.cotp 3882
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-rab 2722  df-v 2972  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-nul 3635  df-if 3789  df-sn 3875  df-pr 3877  df-op 3881  df-ot 3883
This theorem is referenced by:  oteq123d  4071  idafval  14921  coafval  14928  arwlid  14936  arwrid  14937  arwass  14938  efgi  16209  efgtf  16212  efgtval  16213  efgval2  16214  mapdh6bN  35104  mapdh6cN  35105  mapdh6dN  35106  mapdh6gN  35109  hdmap1l6b  35179  hdmap1l6c  35180  hdmap1l6d  35181  hdmap1l6g  35184
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