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Theorem oteq2d 3999
Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
oteq2d  |-  ( ph  -> 
<. C ,  A ,  D >.  =  <. C ,  B ,  D >. )

Proof of Theorem oteq2d
StepHypRef Expression
1 oteq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 oteq2 3996 . 2  |-  ( A  =  B  ->  <. C ,  A ,  D >.  = 
<. C ,  B ,  D >. )
31, 2syl 16 1  |-  ( ph  -> 
<. C ,  A ,  D >.  =  <. C ,  B ,  D >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653   <.cotp 3820
This theorem is referenced by:  oteq123d  4001  mapdh9a  32662  hdmap1eulem  32696  hdmapffval  32701  hdmapfval  32702  hdmapval2  32707
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-ot 3826
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