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Metamath Proof Explorer

Theorem ex-natded5.2-2

Description: A more efficient proof of Theorem 5.2 of Clemente p. 15. Compare with ex-natded5.2 and ex-natded5.2i . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ex-natded5.2.1	$⊢ φ \to ((ψ \land χ) \to θ)$
	ex-natded5.2.2	$⊢ φ \to (χ \to ψ)$
	ex-natded5.2.3	$⊢ φ \to χ$
Assertion	ex-natded5.2-2	$⊢ φ \to θ$

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.2.1	$⊢ φ \to ((ψ \land χ) \to θ)$
2		ex-natded5.2.2	$⊢ φ \to (χ \to ψ)$
3		ex-natded5.2.3	$⊢ φ \to χ$
4	3 2	mpd	$⊢ φ \to ψ$
5	4 3 1	mp2and	$⊢ φ \to θ$