Metamath Proof Explorer


Theorem eqtr2d

Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999)

Ref Expression
Hypotheses eqtr2d.1 φA=B
eqtr2d.2 φB=C
Assertion eqtr2d φC=A

Proof

Step Hyp Ref Expression
1 eqtr2d.1 φA=B
2 eqtr2d.2 φB=C
3 1 2 eqtrd φA=C
4 3 eqcomd φC=A