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Metamath Proof Explorer

Theorem ibar

Description: Introduction of antecedent as conjunct. (Contributed by NM, 5-Dec-1995)

Ref Expression
Assertion ibar ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step Hyp Ref Expression
1 iba ⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜓 ∧ 𝜑 ) ) )
2 1 biancomd ⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) ) )