Theorem tpeq3d 3680

Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)

Hypothesis

Ref	Expression
tpeq1d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
tpeq3d	|- ( ph -> { C , D , A } = { C , D , B } )

Proof of Theorem tpeq3d

Step	Hyp	Ref	Expression
1		tpeq1d.1	. 2 |- ( ph -> A = B )
2		tpeq3 3677	. 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 1353   {ctp 3591

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-un 3131  df-sn 3595  df-tp 3597

This theorem is referenced by:  tpeq123d  3681