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	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ex-natded5.3.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
Assertion	ex-natded5.3-2	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.3.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ex-natded5.3.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3	1 2	syld	$$⊢\phi \to \left(\psi \to \theta \right)$$
4	1 3	jcad	$$⊢\phi \to \left(\psi \to \left(\chi \wedge \theta \right)\right)$$