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Theorem oteq1 3821
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 3812 . . 3  |-  ( A  =  B  ->  <. A ,  C >.  =  <. B ,  C >. )
21opeq1d 3818 . 2  |-  ( A  =  B  ->  <. <. A ,  C >. ,  D >.  = 
<. <. B ,  C >. ,  D >. )
3 df-ot 3663 . 2  |-  <. A ,  C ,  D >.  = 
<. <. A ,  C >. ,  D >.
4 df-ot 3663 . 2  |-  <. B ,  C ,  D >.  = 
<. <. B ,  C >. ,  D >.
52, 3, 43eqtr4g 2353 1  |-  ( A  =  B  ->  <. A ,  C ,  D >.  = 
<. B ,  C ,  D >. )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   <.cop 3656   <.cotp 3657
This theorem is referenced by:  oteq1d  3824  efgi  15044  efgtf  15047  efgtval  15048  mapdh9a  32602  mapdh9aOLDN  32603  hdmapfval  32642  hdmapval2  32647
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-ot 3663
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