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Metamath Proof Explorer

Theorem mpanr12

Description: An inference based on modus ponens. (Contributed by NM, 24-Jul-2009)

Ref Expression
Hypotheses mpanr12.1 ⊢ ψ
mpanr12.2 ⊢ χ
mpanr12.3 ⊢ φ ∧ ψ ∧ χ → θ
Assertion mpanr12 ⊢ φ → θ

Proof

Step Hyp Ref Expression
1 mpanr12.1 ⊢ ψ
2 mpanr12.2 ⊢ χ
3 mpanr12.3 ⊢ φ ∧ ψ ∧ χ → θ
4 1 3 mpanr1 ⊢ φ ∧ χ → θ
5 2 4 mpan2 ⊢ φ → θ