Theorem simp12 986

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

Assertion

Ref	Expression
simp12	⊢ (((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) → ψ)

Proof of Theorem simp12

Step	Hyp	Ref	Expression
1		simp2 956	. 2 ⊢ ((φ ∧ ψ ∧ χ) → ψ)
2	1	3ad2ant1 976	1 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) → ψ)

Syntax hints:   → wi 4   ∧ w3a 934

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  simpl12  1031  simpr12  1040  simp112  1085  simp212  1094  simp312  1103