Metamath Proof Explorer


Theorem syl5reqr

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

Ref Expression
Hypotheses syl5reqr.1
|- B = A
syl5reqr.2
|- ( ph -> B = C )
Assertion syl5reqr
|- ( ph -> C = A )

Proof

Step Hyp Ref Expression
1 syl5reqr.1
 |-  B = A
2 syl5reqr.2
 |-  ( ph -> B = C )
3 1 eqcomi
 |-  A = B
4 3 2 syl5req
 |-  ( ph -> C = A )