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