Theorem simp2ll 1022

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

Assertion

Ref	Expression
simp2ll	⊢ ((θ ∧ ((φ ∧ ψ) ∧ χ) ∧ τ) → φ)

Proof of Theorem simp2ll

Step	Hyp	Ref	Expression
1		simpll 730	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → φ)
2	1	3ad2ant2 977	1 ⊢ ((θ ∧ ((φ ∧ ψ) ∧ χ) ∧ τ) → φ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ 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:  nnpweq  4524  sfinltfin  4536