Theorem simprld

Description: Deduction eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019)

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

Proof

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