Theorem simprrr 741

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

Assertion

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

Proof of Theorem simprrr

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((χ ∧ θ) → θ)
2	1	ad2antll 709	1 ⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → θ)

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:  nnsucelr  4429  ncfinraise  4482  ncfinlower  4484  tfin11  4494  sfindbl  4531  sfintfin  4533  sfinltfin  4536