Theorem ee33an

Description: e33an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee33an.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee33an.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
	ee33an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
Assertion	ee33an	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee33an.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee33an.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
3		ee33an.3	⊢ ( ( 𝜃 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
5	1 2 4	ee33	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )