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Theorem oteq2 3996
Description: Equality theorem for ordered triples. (Contributed by NM, 3-Apr-2015.)
Assertion
Ref Expression
oteq2  |-  ( A  =  B  ->  <. C ,  A ,  D >.  = 
<. C ,  B ,  D >. )

Proof of Theorem oteq2
StepHypRef Expression
1 opeq2 3987 . . 3  |-  ( A  =  B  ->  <. C ,  A >.  =  <. C ,  B >. )
21opeq1d 3992 . 2  |-  ( A  =  B  ->  <. <. C ,  A >. ,  D >.  = 
<. <. C ,  B >. ,  D >. )
3 df-ot 3826 . 2  |-  <. C ,  A ,  D >.  = 
<. <. C ,  A >. ,  D >.
4 df-ot 3826 . 2  |-  <. C ,  B ,  D >.  = 
<. <. C ,  B >. ,  D >.
52, 3, 43eqtr4g 2495 1  |-  ( A  =  B  ->  <. C ,  A ,  D >.  = 
<. C ,  B ,  D >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653   <.cop 3819   <.cotp 3820
This theorem is referenced by:  oteq2d  3999  efgi  15353  efgtf  15356  efgtval  15357  el2wlkonot  28338  el2spthonot  28339  frg2wot1  28448  usg2spot2nb  28456  mapdh9aOLDN  32591  hdmap1eulemOLDN  32625
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 2419
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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-ot 3826
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