Theorem tpeq1d 4075

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

Hypothesis

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

Assertion

Ref	Expression
tpeq1d	|- ( ph -> { A , C , D } = { B , C , D } )

Proof of Theorem tpeq1d

Step	Hyp	Ref	Expression
1		tpeq1d.1	. 2 |- ( ph -> A = B )
2		tpeq1 4072	. 2 |- ( A = B -> { A , C , D } = { B , C , D } )
3	1, 2	syl 17	1 |- ( ph -> { A , C , D } = { B , C , D } )

Syntax hints:   -> wi 4   = wceq 1454   {ctp 3983

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441

This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-v 3058  df-un 3420  df-sn 3980  df-pr 3982  df-tp 3984

This theorem is referenced by:  tpeq123d  4078