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

Metamath Proof Explorer

Theorem mp3an1

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994)

Ref Expression
Hypotheses mp3an1.1 ⊢ φ
mp3an1.2 ⊢ φ ∧ ψ ∧ χ → θ
Assertion mp3an1 ⊢ ψ ∧ χ → θ

Proof

Step Hyp Ref Expression
1 mp3an1.1 ⊢ φ
2 mp3an1.2 ⊢ φ ∧ ψ ∧ χ → θ
3 2 3expb ⊢ φ ∧ ψ ∧ χ → θ
4 1 3 mpan ⊢ ψ ∧ χ → θ