Theorem oteq3d 3719

Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)

Hypothesis

Ref	Expression
oteq1d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
oteq3d	|- ( ph -> <. C , D , A >. = <. C , D , B >. )

Proof of Theorem oteq3d

Step	Hyp	Ref	Expression
1		oteq1d.1	. 2 |- ( ph -> A = B )
2		oteq3 3716	. 2 |- ( A = B -> <. C , D , A >. = <. C , D , B >. )
3	1, 2	syl 14	1 |- ( ph -> <. C , D , A >. = <. C , D , B >. )

Syntax hints:   -> wi 4   = wceq 1331   <.cotp 3531

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-ot 3537

This theorem is referenced by:  oteq123d  3720