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Metamath Proof Explorer

Theorem iba

Description: Introduction of antecedent as conjunct. Theorem *4.73 of WhiteheadRussell p. 121. (Contributed by NM, 30-Mar-1994)

Ref Expression
Assertion iba ⊢ φ → ψ ↔ ψ ∧ φ

Proof

Step Hyp Ref Expression
1 pm3.21 ⊢ φ → ψ → ψ ∧ φ
2 simpl ⊢ ψ ∧ φ → ψ
3 1 2 impbid1 ⊢ φ → ψ ↔ ψ ∧ φ