Theorem ex-natded5.3i 30833

Description: The same as ex-natded5.3 30831 and ex-natded5.3-2 30832 but with no context. Identical to jccir 531, which should be used instead. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

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

Proof of Theorem ex-natded5.3i

Step	Hyp	Ref	Expression
1		ex-natded5.3i.1	. 2 ⊢ (𝜓 → 𝜒)
2		ex-natded5.3i.2	. . 3 ⊢ (𝜒 → 𝜃)
3	1, 2	syl 18	. 2 ⊢ (𝜓 → 𝜃)
4	1, 3	jca 521	1 ⊢ (𝜓 → (𝜒 ∧ 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)