Theorem e11an

Description: Conjunction form of e11 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e11an.1	⊢ (    𝜑    ▶    𝜓    )
	e11an.2	⊢ (    𝜑    ▶    𝜒    )
	e11an.3	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	e11an	⊢ (    𝜑    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e11an.1	⊢ (    𝜑    ▶    𝜓    )
2		e11an.2	⊢ (    𝜑    ▶    𝜒    )
3		e11an.3	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
4	3	ex	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
5	1 2 4	e11	⊢ (    𝜑    ▶    𝜃    )