Theorem simprlr 739

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

Assertion

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

Proof of Theorem simprlr

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((ψ ∧ χ) → χ)
2	1	ad2antrl 708	1 ⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → χ)

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  nnpw1ex  4485  sfinltfin  4536  enprmaplem3  6079