Theorem tpeq1d 4034

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 4031	. 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 1437   {ctp 3945

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408

This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-v 3024  df-un 3384  df-sn 3942  df-pr 3944  df-tp 3946

This theorem is referenced by:  tpeq123d  4037