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Metamath Proof Explorer

Theorem 2thd

Description: Two truths are equivalent. Deduction form. (Contributed by NM, 3-Jun-2012)

Ref Expression
Hypotheses 2thd.1 ⊢ φ → ψ
2thd.2 ⊢ φ → χ
Assertion 2thd ⊢ φ → ψ ↔ χ

Proof

Step Hyp Ref Expression
1 2thd.1 ⊢ φ → ψ
2 2thd.2 ⊢ φ → χ
3 pm5.1im ⊢ ψ → χ → ψ ↔ χ
4 1 2 3 sylc ⊢ φ → ψ ↔ χ