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Metamath Proof Explorer

Theorem mpbid

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses mpbid.min ⊢ ( 𝜑 → 𝜓 )
mpbid.maj ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion mpbid ( 𝜑 → 𝜒 )

Proof

Step Hyp Ref Expression
1 mpbid.min ⊢ ( 𝜑 → 𝜓 )
2 mpbid.maj ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
3 2 biimpd ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4 1 3 mpd ⊢ ( 𝜑 → 𝜒 )