Metamath Proof Explorer


Theorem 3eqtr2d

Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006)

Ref Expression
Hypotheses 3eqtr2d.1 φ A = B
3eqtr2d.2 φ C = B
3eqtr2d.3 φ C = D
Assertion 3eqtr2d φ A = D

Proof

Step Hyp Ref Expression
1 3eqtr2d.1 φ A = B
2 3eqtr2d.2 φ C = B
3 3eqtr2d.3 φ C = D
4 1 2 eqtr4d φ A = C
5 4 3 eqtrd φ A = D