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Metamath Proof Explorer

Theorem mpan2d

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004)

Ref Expression
Hypotheses mpan2d.1 ⊢ φ → χ
mpan2d.2 ⊢ φ → ψ ∧ χ → θ
Assertion mpan2d ⊢ φ → ψ → θ

Proof

Step Hyp Ref Expression
1 mpan2d.1 ⊢ φ → χ
2 mpan2d.2 ⊢ φ → ψ ∧ χ → θ
3 2 expd ⊢ φ → ψ → χ → θ
4 1 3 mpid ⊢ φ → ψ → θ