Theorem ex-natded5.7-2

Description: A more efficient proof of Theorem 5.7 of Clemente p. 19. Compare with ex-natded5.7 . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ex-natded5.7.1	$$⊢\phi \to \left(\psi \vee \left(\chi \wedge \theta \right)\right)$$
Assertion	ex-natded5.7-2	$$⊢\phi \to \left(\psi \vee \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.7.1	$$⊢\phi \to \left(\psi \vee \left(\chi \wedge \theta \right)\right)$$
2		simpl	$$⊢\left(\chi \wedge \theta \right)\to \chi$$
3	2	orim2i	$$⊢\left(\psi \vee \left(\chi \wedge \theta \right)\right)\to \left(\psi \vee \chi \right)$$
4	1 3	syl	$$⊢\phi \to \left(\psi \vee \chi \right)$$