Theorem simp213 1095

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp213	⊢ ((η ∧ ((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) ∧ ζ) → χ)

Proof of Theorem simp213

Step	Hyp	Ref	Expression
1		simp13 987	. 2 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) → χ)
2	1	3ad2ant2 977	1 ⊢ ((η ∧ ((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) ∧ ζ) → χ)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by: (None)