Theorem e10an

Description: Conjunction form of e10 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e10an.1	⊢ (    𝜑    ▶    𝜓    )
	e10an.2	⊢ 𝜒
	e10an.3	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	e10an	⊢ (    𝜑    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e10an.1	⊢ (    𝜑    ▶    𝜓    )
2		e10an.2	⊢ 𝜒
3		e10an.3	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
4	3	ex	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
5	1 2 4	e10	⊢ (    𝜑    ▶    𝜃    )