Theorem e02an

Description: Conjunction form of e02 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e02an.1	⊢ 𝜑
	e02an.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
	e02an.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
Assertion	e02an	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e02an.1	⊢ 𝜑
2		e02an.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
3		e02an.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
5	1 2 4	e02	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )