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Theorem oteq3d 3958
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 3955 . 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 3778
This theorem is referenced by:  oteq123d  3959  idafval  14167  coafval  14174  arwlid  14182  arwrid  14183  arwass  14184  efgi  15306  efgtf  15309  efgtval  15310  efgval2  15311  mapdh6bN  32220  mapdh6cN  32221  mapdh6dN  32222  mapdh6gN  32225  hdmap1l6b  32295  hdmap1l6c  32296  hdmap1l6d  32297  hdmap1l6g  32300
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
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 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-ot 3784
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