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Theorem oteq1d 3988
Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
oteq1d  |-  ( ph  -> 
<. A ,  C ,  D >.  =  <. B ,  C ,  D >. )

Proof of Theorem oteq1d
StepHypRef Expression
1 oteq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 oteq1 3985 . 2  |-  ( A  =  B  ->  <. A ,  C ,  D >.  = 
<. B ,  C ,  D >. )
31, 2syl 16 1  |-  ( ph  -> 
<. A ,  C ,  D >.  =  <. B ,  C ,  D >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   <.cotp 3810
This theorem is referenced by:  oteq123d  3991  hdmapfval  32555
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-ot 3816
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