Metamath Proof Explorer


Theorem bj-mp2c

Description: A doublemodus ponens inference. Inference associated with mpd . (Contributed by BJ, 24-Sep-2019)

Ref Expression
Hypotheses bj-mp2c.majm ⊢ φ → ψ → χ
bj-mp2c.maj ⊢ φ → ψ
bj-mp2c.min ⊢ φ
Assertion bj-mp2c ⊢ χ

Proof

Step Hyp Ref Expression
1 bj-mp2c.majm ⊢ φ → ψ → χ
2 bj-mp2c.maj ⊢ φ → ψ
3 bj-mp2c.min ⊢ φ
4 3 2 ax-mp ⊢ ψ
5 3 4 1 mp2 ⊢ χ