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