Theorem simp1l 979

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)

Assertion

Ref	Expression
simp1l	⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → φ)

Proof of Theorem simp1l

Step	Hyp	Ref	Expression
1		simpl 443	. 2 ⊢ ((φ ∧ ψ) → φ)
2	1	3ad2ant1 976	1 ⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → 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:  simpl1l  1006  simpr1l  1012  simp11l  1066  simp21l  1072  simp31l  1078  ncfindi  4476  tfinpw1  4495  tfinltfinlem1  4501  nnpweq  4524  sfintfin  4533  sfinltfin  4536