Theorem mp3anr1 1274

Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006.)

Hypotheses

Ref	Expression
mp3anr1.1	⊢ ψ
mp3anr1.2	⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)

Assertion

Ref	Expression
mp3anr1	⊢ ((φ ∧ (χ ∧ θ)) → τ)

Proof of Theorem mp3anr1

Step	Hyp	Ref	Expression
1		mp3anr1.1	. . 3 ⊢ ψ
2		mp3anr1.2	. . . 4 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)
3	2	ancoms 439	. . 3 ⊢ (((ψ ∧ χ ∧ θ) ∧ φ) → τ)
4	1, 3	mp3anl1 1271	. 2 ⊢ (((χ ∧ θ) ∧ φ) → τ)
5	4	ancoms 439	1 ⊢ ((φ ∧ (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: (None)