Metamath Proof Explorer

Theorem syl5req

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)

Ref Expression
Hypotheses syl5req.1 
|- A = B
syl5req.2 
|- ( ph -> B = C )
Assertion syl5req 
|- ( ph -> C = A )

Proof

Step Hyp Ref Expression
1 syl5req.1 
 |-  A = B
2 syl5req.2 
 |-  ( ph -> B = C )
3 1 2 syl5eq 
 |-  ( ph -> A = C )
4 3 eqcomd 
 |-  ( ph -> C = A )