Theorem e21an

Description: Conjunction form of e21 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e21an.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e21an.2	⊢ (    𝜑    ▶    𝜃    )
	e21an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
Assertion	e21an	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e21an.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e21an.2	⊢ (    𝜑    ▶    𝜃    )
3		e21an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
5	1 2 4	e21	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )