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Theorem oteq3d 3940
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 3937 . 2  |-  ( A  =  B  ->  <. C ,  D ,  A >.  = 
<. C ,  D ,  B >. )
31, 2syl 16 1  |-  ( ph  -> 
<. C ,  D ,  A >.  =  <. C ,  D ,  B >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   <.cotp 3761
This theorem is referenced by:  oteq123d  3941  idafval  14139  coafval  14146  arwlid  14154  arwrid  14155  arwass  14156  efgi  15278  efgtf  15281  efgtval  15282  efgval2  15283  mapdh6bN  31852  mapdh6cN  31853  mapdh6dN  31854  mapdh6gN  31857  hdmap1l6b  31927  hdmap1l6c  31928  hdmap1l6d  31929  hdmap1l6g  31932
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-ot 3767
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