Theorem simp23 990

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)

Assertion

Ref	Expression
simp23	⊢ ((φ ∧ (ψ ∧ χ ∧ θ) ∧ τ) → θ)

Proof of Theorem simp23

Step	Hyp	Ref	Expression
1		simp3 957	. 2 ⊢ ((ψ ∧ χ ∧ θ) → θ)
2	1	3ad2ant2 977	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ) ∧ τ) → θ)

Syntax hints:   → wi 4   ∧ 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:  simpl23  1035  simpr23  1044  simp123  1089  simp223  1098  simp323  1107  sfinltfin  4536