Theorem ex-natded5.2i 30787

Description: The same as ex-natded5.2 30785 and ex-natded5.2-2 30786 but with no context. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
ex-natded5.2i	⊢ 𝜃

Proof of Theorem ex-natded5.2i

Step	Hyp	Ref	Expression
1		ex-natded5.2i.3	. . . 4 ⊢ 𝜒
2		ex-natded5.2i.2	. . . 4 ⊢ (𝜒 → 𝜓)
3	1, 2	ax-mp 5	. . 3 ⊢ 𝜓
4	3, 1	pm3.2i 476	. 2 ⊢ (𝜓 ∧ 𝜒)
5		ex-natded5.2i.1	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃)
6	4, 5	ax-mp 5	1 ⊢ 𝜃

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by: (None)