Theorem mpanr1 664

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
mpanr1.1	⊢ ψ
mpanr1.2	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Assertion

Ref	Expression
mpanr1	⊢ ((φ ∧ χ) → θ)

Proof of Theorem mpanr1

Step	Hyp	Ref	Expression
1		mpanr1.1	. 2 ⊢ ψ
2		mpanr1.2	. . 3 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	2	anassrs 629	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
4	1, 3	mpanl2 662	1 ⊢ ((φ ∧ 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:  mpanr12  666