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Theorem oteq2d 4156
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 4153 . 2  |-  ( A  =  B  ->  <. C ,  A ,  D >.  = 
<. C ,  B ,  D >. )
31, 2syl 16 1  |-  ( ph  -> 
<. C ,  A ,  D >.  =  <. C ,  B ,  D >. )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1370   <.cotp 3969
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-ext 2429
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1702  df-clab 2436  df-cleq 2442  df-clel 2445  df-nfc 2598  df-rab 2801  df-v 3056  df-dif 3415  df-un 3417  df-in 3419  df-ss 3426  df-nul 3722  df-if 3876  df-sn 3962  df-pr 3964  df-op 3968  df-ot 3970
This theorem is referenced by:  oteq123d  4158  mapdh9a  35717  hdmap1eulem  35751  hdmapffval  35756  hdmapfval  35757  hdmapval2  35762
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