Theorem mpanl12 663

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005.)

Hypotheses

Ref	Expression
mpanl12.1	⊢ φ
mpanl12.2	⊢ ψ
mpanl12.3	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

Ref	Expression
mpanl12	⊢ (χ → θ)

Proof of Theorem mpanl12

Step	Hyp	Ref	Expression
1		mpanl12.2	. 2 ⊢ ψ
2		mpanl12.1	. . 3 ⊢ φ
3		mpanl12.3	. . 3 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
4	2, 3	mpanl1 661	. 2 ⊢ ((ψ ∧ χ) → θ)
5	1, 4	mpan 651	1 ⊢ (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:  reuun1  3538  funprg  5150  mucnc  6132