Theorem simprrd

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

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

Proof

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