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Theorem oteq1 3805
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 3796 . . 3  |-  ( A  =  B  ->  <. A ,  C >.  =  <. B ,  C >. )
21opeq1d 3802 . 2  |-  ( A  =  B  ->  <. <. A ,  C >. ,  D >.  = 
<. <. B ,  C >. ,  D >. )
3 df-ot 3650 . 2  |-  <. A ,  C ,  D >.  = 
<. <. A ,  C >. ,  D >.
4 df-ot 3650 . 2  |-  <. B ,  C ,  D >.  = 
<. <. B ,  C >. ,  D >.
52, 3, 43eqtr4g 2340 1  |-  ( A  =  B  ->  <. A ,  C ,  D >.  = 
<. B ,  C ,  D >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   <.cop 3643   <.cotp 3644
This theorem is referenced by:  oteq1d  3808  efgi  15028  efgtf  15031  efgtval  15032  mapdh9a  31353  mapdh9aOLDN  31354  hdmapfval  31393  hdmapval2  31398
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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