Theorem ee30an

Description: Conjunction form of ee30 . (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee30an.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee30an.2	⊢ 𝜏
	ee30an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
Assertion	ee30an	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee30an.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee30an.2	⊢ 𝜏
3		ee30an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
5	1 2 4	ee30	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )