Theorem simp11 985

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

Assertion

Ref	Expression
simp11	⊢ (((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) → φ)

Proof of Theorem simp11

Step	Hyp	Ref	Expression
1		simp1 955	. 2 ⊢ ((φ ∧ ψ ∧ χ) → φ)
2	1	3ad2ant1 976	1 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) → φ)

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:  simpl11  1030  simpr11  1039  simp111  1084  simp211  1093  simp311  1102