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Metamath Proof Explorer

Theorem pm5.1

Description: Two propositions are equivalent if they are both true. Theorem *5.1 of WhiteheadRussell p. 123. (Contributed by NM, 21-May-1994)

Ref Expression
Assertion pm5.1 ⊢ φ ∧ ψ → φ ↔ ψ

Proof

Step Hyp Ref Expression
1 pm5.501 ⊢ φ → ψ ↔ φ ↔ ψ
2 1 biimpa ⊢ φ ∧ ψ → φ ↔ ψ