Metamath Proof Explorer


Theorem syl6eq

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

Ref Expression
Hypotheses syl6eq.1
|- ( ph -> A = B )
syl6eq.2
|- B = C
Assertion syl6eq
|- ( ph -> A = C )

Proof

Step Hyp Ref Expression
1 syl6eq.1
 |-  ( ph -> A = B )
2 syl6eq.2
 |-  B = C
3 2 a1i
 |-  ( ph -> B = C )
4 1 3 eqtrd
 |-  ( ph -> A = C )