Theorem simp2r 982

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)

Assertion

Ref	Expression
simp2r	⊢ ((φ ∧ (ψ ∧ χ) ∧ θ) → χ)

Proof of Theorem simp2r

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((ψ ∧ χ) → χ)
2	1	3ad2ant2 977	1 ⊢ ((φ ∧ (ψ ∧ χ) ∧ θ) → χ)

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:  simpl2r  1009  simpr2r  1015  simp12r  1069  simp22r  1075  simp32r  1081  tfin11  4494  tfinpw1  4495  tfinltfinlem1  4501  nnadjoinpw  4522  funprgOLD  5151  f1oiso2  5501  enadjlem1  6060