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Metamath Proof Explorer

Theorem sylan9eqr

Description: An equality transitivity deduction. (Contributed by NM, 8-May-1994)

Ref Expression
Hypotheses sylan9eqr.1 ⊢ φ → A = B
sylan9eqr.2 ⊢ ψ → B = C
Assertion sylan9eqr ⊢ ψ ∧ φ → A = C

Proof

Step Hyp Ref Expression
1 sylan9eqr.1 ⊢ φ → A = B
2 sylan9eqr.2 ⊢ ψ → B = C
3 1 2 sylan9eq ⊢ φ ∧ ψ → A = C
4 3 ancoms ⊢ ψ ∧ φ → A = C