This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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