Theorem simp3i 966

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (φ ∧ ψ ∧ χ)

Assertion

Ref	Expression
simp3i	⊢ χ

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (φ ∧ ψ ∧ χ)
2		simp3 957	. 2 ⊢ ((φ ∧ ψ ∧ χ) → χ)
3	1, 2	ax-mp 5	1 ⊢ χ

Syntax hints:   ∧ 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: (None)