Theorem ee32

Description: e32 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee32.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee32.2	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
	ee32.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
Assertion	ee32	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee32.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee32.2	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
3		ee32.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
4	2	a1dd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
5	1 4 3	ee33	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )