Theorem simprd

Description: Deduction eliminating a conjunct. (Contributed by NM, 14-May-1993) A translation of natural deduction rule /\ ER ( /\ elimination right), see natded . (Proof shortened by Wolf Lammen, 3-Oct-2013)

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

Proof

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