Theorem simp3d 969

Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.)

Hypothesis

Ref	Expression
3simp1d.1	⊢ (φ → (ψ ∧ χ ∧ θ))

Assertion

Ref	Expression
simp3d	⊢ (φ → θ)

Proof of Theorem simp3d

Step	Hyp	Ref	Expression
1		3simp1d.1	. 2 ⊢ (φ → (ψ ∧ χ ∧ θ))
2		simp3 957	. 2 ⊢ ((ψ ∧ χ ∧ θ) → θ)
3	1, 2	syl 15	1 ⊢ (φ → θ)

Syntax hints:   → wi 4   ∧ 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:  simp3bi  972