Theorem simp322 1106

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

Assertion

Ref	Expression
simp322	⊢ ((η ∧ ζ ∧ (θ ∧ (φ ∧ ψ ∧ χ) ∧ τ)) → ψ)

Proof of Theorem simp322

Step	Hyp	Ref	Expression
1		simp22 989	. 2 ⊢ ((θ ∧ (φ ∧ ψ ∧ χ) ∧ τ) → ψ)
2	1	3ad2ant3 978	1 ⊢ ((η ∧ ζ ∧ (θ ∧ (φ ∧ ψ ∧ χ) ∧ τ)) → ψ)

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)