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Metamath Proof Explorer

Theorem sylan9req

Description: An equality transitivity deduction. (Contributed by NM, 23-Jun-2007)

Ref Expression
Hypotheses sylan9req.1 ⊢ φ → B = A
sylan9req.2 ⊢ ψ → B = C
Assertion sylan9req ⊢ φ ∧ ψ → A = C

Proof

Step Hyp Ref Expression
1 sylan9req.1 ⊢ φ → B = A
2 sylan9req.2 ⊢ ψ → B = C
3 1 eqcomd ⊢ φ → A = B
4 3 2 sylan9eq ⊢ φ ∧ ψ → A = C