Theorem simp31 991

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

Assertion

Ref	Expression
simp31	⊢ ((φ ∧ ψ ∧ (χ ∧ θ ∧ τ)) → χ)

Proof of Theorem simp31

Step	Hyp	Ref	Expression
1		simp1 955	. 2 ⊢ ((χ ∧ θ ∧ τ) → χ)
2	1	3ad2ant3 978	1 ⊢ ((φ ∧ ψ ∧ (χ ∧ θ ∧ τ)) → χ)

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:  simpl31  1036  simpr31  1045  simp131  1090  simp231  1099  simp331  1108  tfin11  4494