Theorem simplbi

Description: Deduction eliminating a conjunct. (Contributed by NM, 27-May-1998)

	Ref	Expression
Hypothesis	simplbi.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
Assertion	simplbi	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		simplbi.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
2	1	biimpi	$$⊢\phi \to \left(\psi \wedge \chi \right)$$
3	2	simpld	$$⊢\phi \to \psi$$