Metamath Proof Explorer

Theorem syl5eq

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses syl5eq.1 
|- A = B
syl5eq.2 
|- ( ph -> B = C )
Assertion syl5eq 
|- ( ph -> A = C )

Proof

Step Hyp Ref Expression
1 syl5eq.1 
 |-  A = B
2 syl5eq.2 
 |-  ( ph -> B = C )
3 1 a1i 
 |-  ( ph -> A = B )
4 3 2 eqtrd 
 |-  ( ph -> A = C )