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Theorem oteq2d 4216
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 4213 . 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 1398   <.cotp 4024
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-ot 4025
This theorem is referenced by:  oteq123d  4218  mapdh9a  37933  mapdh9aOLDN  37934  hdmap1eulem  37967  hdmap1eulemOLDN  37968  hdmapffval  37972  hdmapfval  37973  hdmapval2  37978
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