Theorem simplll 734

Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.)

Assertion

Ref	Expression
simplll	⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → φ)

Proof of Theorem simplll

Step	Hyp	Ref	Expression
1		simpl 443	. 2 ⊢ ((φ ∧ ψ) → φ)
2	1	ad2antrr 706	1 ⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → φ)

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:  simp-4l  742  prepeano4  4452  nnpw1ex  4485  tfindi  4497  evenodddisj  4517  enprmaplem3  6079