Metamath Proof Explorer

Theorem syl5eqr

Description: An equality transitivity deduction. (Contributed by NM, 5-Aug-1993)

Ref Expression
Hypotheses syl5eqr.1 
|- B = A
syl5eqr.2 
|- ( ph -> B = C )
Assertion syl5eqr 
|- ( ph -> A = C )

Proof

Step Hyp Ref Expression
1 syl5eqr.1 
 |-  B = A
2 syl5eqr.2 
 |-  ( ph -> B = C )
3 1 eqcomi 
 |-  A = B
4 3 2 syl5eq 
 |-  ( ph -> A = C )