Theorem simpld

Description: Deduction eliminating a conjunct. A translation of natural deduction rule /\ EL ( /\ elimination left), see natded . (Contributed by NM, 26-May-1993)

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

Proof

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