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Metamath Proof Explorer

Theorem ex-natded5.3-2

Description: A more efficient proof of Theorem 5.3 of Clemente p. 16. Compare with ex-natded5.3 and ex-natded5.3i . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ex-natded5.3.1	$⊢ φ \to (ψ \to χ)$
	ex-natded5.3.2	$⊢ φ \to (χ \to θ)$
Assertion	ex-natded5.3-2	$⊢ φ \to (ψ \to (χ \land θ))$

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.3.1	$⊢ φ \to (ψ \to χ)$
2		ex-natded5.3.2	$⊢ φ \to (χ \to θ)$
3	1 2	syld	$⊢ φ \to (ψ \to θ)$
4	1 3	jcad	$⊢ φ \to (ψ \to (χ \land θ))$