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Theorem oteq3 4181
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 4171 . 2  |-  ( A  =  B  ->  <. <. C ,  D >. ,  A >.  = 
<. <. C ,  D >. ,  B >. )
2 df-ot 3997 . 2  |-  <. C ,  D ,  A >.  = 
<. <. C ,  D >. ,  A >.
3 df-ot 3997 . 2  |-  <. C ,  D ,  B >.  = 
<. <. C ,  D >. ,  B >.
41, 2, 33eqtr4g 2520 1  |-  ( A  =  B  ->  <. C ,  D ,  A >.  = 
<. C ,  D ,  B >. )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1370   <.cop 3994   <.cotp 3996
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 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
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 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-ot 3997
This theorem is referenced by:  oteq3d  4184  efgi0  16341  efgi1  16342  otsndisj  30299  otiunsndisj  30300  otiunsndisjX  30301  mapdhcl  35730  mapdh6dN  35742  mapdh8  35792  mapdh9a  35793  mapdh9aOLDN  35794  hdmap1l6d  35817  hdmapval  35834  hdmapval2  35838  hdmapval3N  35844
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