Theorem ee23an

Description: e23an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee23an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee23an.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
	ee23an.3	⊢ ( ( 𝜒 ∧ 𝜏 ) → 𝜂 )
Assertion	ee23an	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee23an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee23an.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
3		ee23an.3	⊢ ( ( 𝜒 ∧ 𝜏 ) → 𝜂 )
4	1	a1dd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )
5	4 2 3	ee33an	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜂 ) ) )