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Theorem oteq3 3995
Description: Equality theorem for ordered triples. (Contributed by NM, 3-Apr-2015.)
Assertion
Ref Expression
oteq3  |-  ( A  =  B  ->  <. C ,  D ,  A >.  = 
<. C ,  D ,  B >. )

Proof of Theorem oteq3
StepHypRef Expression
1 opeq2 3985 . 2  |-  ( A  =  B  ->  <. <. C ,  D >. ,  A >.  = 
<. <. C ,  D >. ,  B >. )
2 df-ot 3824 . 2  |-  <. C ,  D ,  A >.  = 
<. <. C ,  D >. ,  A >.
3 df-ot 3824 . 2  |-  <. C ,  D ,  B >.  = 
<. <. C ,  D >. ,  B >.
41, 2, 33eqtr4g 2493 1  |-  ( A  =  B  ->  <. C ,  D ,  A >.  = 
<. C ,  D ,  B >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   <.cop 3817   <.cotp 3818
This theorem is referenced by:  oteq3d  3998  efgi0  15352  efgi1  15353  otsndisj  28065  otiunsndisj  28066  otiunsndisjX  28067  mapdhcl  32525  mapdh6dN  32537  mapdh8  32587  mapdh9a  32588  mapdh9aOLDN  32589  hdmap1l6d  32612  hdmapval  32629  hdmapval2  32633  hdmapval3N  32639
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 2417
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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-ot 3824
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