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Metamath Proof Explorer

Theorem mpanr1

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

Ref Expression
Hypotheses mpanr1.1 ⊢ ψ
mpanr1.2 ⊢ φ ∧ ψ ∧ χ → θ
Assertion mpanr1 ⊢ φ ∧ χ → θ

Proof

Step Hyp Ref Expression
1 mpanr1.1 ⊢ ψ
2 mpanr1.2 ⊢ φ ∧ ψ ∧ χ → θ
3 2 anassrs ⊢ φ ∧ ψ ∧ χ → θ
4 1 3 mpanl2 ⊢ φ ∧ χ → θ