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Theorem oteq1 3994
Description: Equality theorem for ordered triples. (Contributed by NM, 3-Apr-2015.)
Assertion
Ref Expression
oteq1  |-  ( A  =  B  ->  <. A ,  C ,  D >.  = 
<. B ,  C ,  D >. )

Proof of Theorem oteq1
StepHypRef Expression
1 opeq1 3985 . . 3  |-  ( A  =  B  ->  <. A ,  C >.  =  <. B ,  C >. )
21opeq1d 3991 . 2  |-  ( A  =  B  ->  <. <. A ,  C >. ,  D >.  = 
<. <. B ,  C >. ,  D >. )
3 df-ot 3825 . 2  |-  <. A ,  C ,  D >.  = 
<. <. A ,  C >. ,  D >.
4 df-ot 3825 . 2  |-  <. B ,  C ,  D >.  = 
<. <. B ,  C >. ,  D >.
52, 3, 43eqtr4g 2494 1  |-  ( A  =  B  ->  <. A ,  C ,  D >.  = 
<. B ,  C ,  D >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653   <.cop 3818   <.cotp 3819
This theorem is referenced by:  oteq1d  3997  efgi  15352  efgtf  15355  efgtval  15356  otiunsndisj  28067  otiunsndisjX  28068  mapdh9a  32589  mapdh9aOLDN  32590  hdmapval2  32634
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-ot 3825
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