Theorem mpan2i 658

Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)

Hypotheses

Ref	Expression
mpan2i.1	⊢ χ
mpan2i.2	⊢ (φ → ((ψ ∧ χ) → θ))

Assertion

Ref	Expression
mpan2i	⊢ (φ → (ψ → θ))

Proof of Theorem mpan2i

Step	Hyp	Ref	Expression
1		mpan2i.1	. . 3 ⊢ χ
2	1	a1i 10	. 2 ⊢ (φ → χ)
3		mpan2i.2	. 2 ⊢ (φ → ((ψ ∧ χ) → θ))
4	2, 3	mpan2d 655	1 ⊢ (φ → (ψ → θ))

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by: (None)