Theorem mpanl2 662

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
mpanl2.1	⊢ ψ
mpanl2.2	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

Ref	Expression
mpanl2	⊢ ((φ ∧ χ) → θ)

Proof of Theorem mpanl2

Step	Hyp	Ref	Expression
1		mpanl2.1	. . 3 ⊢ ψ
2	1	jctr 526	. 2 ⊢ (φ → (φ ∧ ψ))
3		mpanl2.2	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
4	2, 3	sylan 457	1 ⊢ ((φ ∧ χ) → 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:  mpanr1  664  mp3an2  1265  reuss  3536  vfinncsp  4554