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

Metamath Proof Explorer

Theorem mpanl1

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Wolf Lammen, 7-Apr-2013)

Ref Expression
Hypotheses mpanl1.1 ⊢ 𝜑
mpanl1.2 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion mpanl1 ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 mpanl1.1 ⊢ 𝜑
2 mpanl1.2 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
3 1 jctl ⊢ ( 𝜓 → ( 𝜑 ∧ 𝜓 ) )
4 3 2 sylan ⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )