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Metamath Proof Explorer

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	$⊢ φ \to (ψ \lor (χ \land θ))$
	Assertion	ex-natded5.7-2	$⊢ φ \to (ψ \lor χ)$

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.7.1	$⊢ φ \to (ψ \lor (χ \land θ))$
2		simpl	$⊢ (χ \land θ) \to χ$
3	2	orim2i	$⊢ (ψ \lor (χ \land θ)) \to (ψ \lor χ)$
4	1 3	syl	$⊢ φ \to (ψ \lor χ)$