Metamath Proof Explorer


Theorem bj-mp2d

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

Ref Expression
Hypotheses bj-mp2d.majm ⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
bj-mp2d.maj ⊢ ( 𝜑 → 𝜓 )
bj-mp2d.min ⊢ 𝜑
Assertion bj-mp2d 𝜒

Proof

Step Hyp Ref Expression
1 bj-mp2d.majm ⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
2 bj-mp2d.maj ⊢ ( 𝜑 → 𝜓 )
3 bj-mp2d.min ⊢ 𝜑
4 3 2 ax-mp ⊢ 𝜓
5 4 3 1 mp2 ⊢ 𝜒