Theorem oteq3d 4416

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 4413	. 2 |- ( A = B -> <. C , D , A >. = <. C , D , B >. )
3	1, 2	syl 17	1 |- ( ph -> <. C , D , A >. = <. C , D , B >. )

Syntax hints:   -> wi 4   = wceq 1483   <.cotp 4185

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-ot 4186

This theorem is referenced by:  oteq123d  4417  idafval  16707  coafval  16714  arwlid  16722  arwrid  16723  arwass  16724  efgi  18132  efgtf  18135  efgtval  18136  efgval2  18137  mapdh6bN  37026  mapdh6cN  37027  mapdh6dN  37028  mapdh6gN  37031  hdmap1l6b  37101  hdmap1l6c  37102  hdmap1l6d  37103  hdmap1l6g  37106