Theorem simp2l 981

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

Assertion

Ref	Expression
simp2l	⊢ ((φ ∧ (ψ ∧ χ) ∧ θ) → ψ)

Proof of Theorem simp2l

Step	Hyp	Ref	Expression
1		simpl 443	. 2 ⊢ ((ψ ∧ χ) → ψ)
2	1	3ad2ant2 977	1 ⊢ ((φ ∧ (ψ ∧ χ) ∧ θ) → ψ)

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:  simpl2l  1008  simpr2l  1014  simp12l  1068  simp22l  1074  simp32l  1080  nnsucelr  4429  tfin11  4494  funprgOLD  5151  f1oiso2  5501  enadjlem1  6060