Metamath Proof Explorer


Theorem eqtr2di

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

Ref Expression
Hypotheses eqtr2di.1
|- ( ph -> A = B )
eqtr2di.2
|- B = C
Assertion eqtr2di
|- ( ph -> C = A )

Proof

Step Hyp Ref Expression
1 eqtr2di.1
 |-  ( ph -> A = B )
2 eqtr2di.2
 |-  B = C
3 1 2 eqtrdi
 |-  ( ph -> A = C )
4 3 eqcomd
 |-  ( ph -> C = A )