Theorem ee03an

Description: Conjunction form of ee03 . (Contributed by Alan Sare, 18-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee03an.1	⊢ 𝜑
	ee03an.2	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
	ee03an.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
Assertion	ee03an	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee03an.1	⊢ 𝜑
2		ee03an.2	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
3		ee03an.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
5	1 2 4	ee03	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )