Theorem ex-natded5.2i

Description: The same as ex-natded5.2 and ex-natded5.2-2 but with no context. (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ex-natded5.2i.1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
	ex-natded5.2i.2	⊢ ( 𝜒 → 𝜓 )
	ex-natded5.2i.3	⊢ 𝜒
Assertion	ex-natded5.2i	⊢ 𝜃

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.2i.1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
2		ex-natded5.2i.2	⊢ ( 𝜒 → 𝜓 )
3		ex-natded5.2i.3	⊢ 𝜒
4	3 2	ax-mp	⊢ 𝜓
5	4 3	pm3.2i	⊢ ( 𝜓 ∧ 𝜒 )
6	5 1	ax-mp	⊢ 𝜃