Theorem e01an

Description: Conjunction form of e01 . (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e01an.1	⊢ 𝜑
	e01an.2	⊢ (    𝜓    ▶    𝜒    )
	e01an.3	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
Assertion	e01an	⊢ (    𝜓    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e01an.1	⊢ 𝜑
2		e01an.2	⊢ (    𝜓    ▶    𝜒    )
3		e01an.3	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
4	3	ex	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
5	1 2 4	e01	⊢ (    𝜓    ▶    𝜃    )