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Metamath Proof Explorer

Theorem mpand

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004) (Proof shortened by Wolf Lammen, 7-Apr-2013)

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

Proof

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