Theorem mp3anl1 1271

Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)

Hypotheses

Ref	Expression
mp3anl1.1	⊢ φ
mp3anl1.2	⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → τ)

Assertion

Ref	Expression
mp3anl1	⊢ (((ψ ∧ χ) ∧ θ) → τ)

Proof of Theorem mp3anl1

Step	Hyp	Ref	Expression
1		mp3anl1.1	. . 3 ⊢ φ
2		mp3anl1.2	. . . 4 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → τ)
3	2	ex 423	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → (θ → τ))
4	1, 3	mp3an1 1264	. 2 ⊢ ((ψ ∧ χ) → (θ → τ))
5	4	imp 418	1 ⊢ (((ψ ∧ χ) ∧ θ) → τ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by:  mp3anr1  1274