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Theorem oteq2d 3932
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 3929 . 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 1649   <.cotp 3754
This theorem is referenced by:  oteq123d  3934  mapdh9a  31956  hdmap1eulem  31990  hdmapffval  31995  hdmapfval  31996  hdmapval2  32001
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
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 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-ot 3760
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