Theorem simplld

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

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

Proof

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