Theorem simpl1l 1006

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

Assertion

Ref	Expression
simpl1l	⊢ ((((φ ∧ ψ) ∧ χ ∧ θ) ∧ τ) → φ)

Proof of Theorem simpl1l

Step	Hyp	Ref	Expression
1		simp1l 979	. 2 ⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → φ)
2	1	adantr 451	1 ⊢ ((((φ ∧ ψ) ∧ χ ∧ θ) ∧ τ) → φ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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

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

This theorem is referenced by:  tfin11  4494  sfinltfin  4536