Theorem simplrr 737

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

Assertion

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

Proof of Theorem simplrr

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((ψ ∧ χ) → χ)
2	1	ad2antlr 707	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:  pm2.61da3ne  2597  rmob  3135  preaddccan2  4456  ncfinraise  4482  tfindi  4497  evenodddisj  4517  tfinnn  4535  enprmaplem3  6079  ncdisjun  6137