Theorem simp1rl 1020

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

Assertion

Ref	Expression
simp1rl	⊢ (((χ ∧ (φ ∧ ψ)) ∧ θ ∧ τ) → φ)

Proof of Theorem simp1rl

Step	Hyp	Ref	Expression
1		simprl 732	. 2 ⊢ ((χ ∧ (φ ∧ ψ)) → φ)
2	1	3ad2ant1 976	1 ⊢ (((χ ∧ (φ ∧ ψ)) ∧ θ ∧ 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:  nnpw1ex  4485  sfin112  4530