Theorem mpanl1 661

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

Hypotheses

Ref	Expression
mpanl1.1	⊢ φ
mpanl1.2	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

Ref	Expression
mpanl1	⊢ ((ψ ∧ χ) → θ)

Proof of Theorem mpanl1

Step	Hyp	Ref	Expression
1		mpanl1.1	. . 3 ⊢ φ
2	1	jctl 525	. 2 ⊢ (ψ → (φ ∧ ψ))
3		mpanl1.2	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
4	2, 3	sylan 457	1 ⊢ ((ψ ∧ χ) → θ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  mpanl12  663