Theorem e03an

Description: Conjunction form of e03 . (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e03an.1	⊢ 𝜑
	e03an.2	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
	e03an.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
Assertion	e03an	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e03an.1	⊢ 𝜑
2		e03an.2	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
3		e03an.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
5	1 2 4	e03	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )