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Metamath Proof Explorer

Theorem mpanl2

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

Ref Expression
Hypotheses mpanl2.1 ⊢ ψ
mpanl2.2 ⊢ φ ∧ ψ ∧ χ → θ
Assertion mpanl2 ⊢ φ ∧ χ → θ

Proof

Step Hyp Ref Expression
1 mpanl2.1 ⊢ ψ
2 mpanl2.2 ⊢ φ ∧ ψ ∧ χ → θ
3 1 jctr ⊢ φ → φ ∧ ψ
4 3 2 sylan ⊢ φ ∧ χ → θ