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Metamath Proof Explorer

Theorem tpeq1d

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

Ref Expression
Hypothesis tpeq1d.1 
|- ( ph -> A = B )
Assertion tpeq1d 
|- ( ph -> { A , C , D } = { B , C , D } )

Proof

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