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Theorem oteq3 3807
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 3797 . 2  |-  ( A  =  B  ->  <. <. C ,  D >. ,  A >.  = 
<. <. C ,  D >. ,  B >. )
2 df-ot 3650 . 2  |-  <. C ,  D ,  A >.  = 
<. <. C ,  D >. ,  A >.
3 df-ot 3650 . 2  |-  <. C ,  D ,  B >.  = 
<. <. C ,  D >. ,  B >.
41, 2, 33eqtr4g 2340 1  |-  ( A  =  B  ->  <. C ,  D ,  A >.  = 
<. C ,  D ,  B >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   <.cop 3643   <.cotp 3644
This theorem is referenced by:  oteq3d  3810  efgi  15028  efgi0  15029  efgi1  15030  efgtf  15031  efgtval  15032  efgval2  15033  mapdhcl  31917  mapdh6bN  31927  mapdh6cN  31928  mapdh6dN  31929  mapdh6gN  31932  mapdh8  31979  mapdh9a  31980  mapdh9aOLDN  31981  hdmap1l6b  32002  hdmap1l6c  32003  hdmap1l6d  32004  hdmap1l6g  32007  hdmapval  32021  hdmapval2  32025  hdmapval3N  32031
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-ot 3650
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