Theorem simp1i 964

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
simp1i	⊢ φ

Proof of Theorem simp1i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (φ ∧ ψ ∧ χ)
2		simp1 955	. 2 ⊢ ((φ ∧ ψ ∧ χ) → φ)
3	1, 2	ax-mp 5	1 ⊢ φ

This proof depends on syntax axioms:   ∧ 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: (None)