Theorem ee323

Description: e323 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee323.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee323.2	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
	ee323.3	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )
	ee323.4	⊢ ( 𝜃 → ( 𝜏 → ( 𝜂 → 𝜁 ) ) )
Assertion	ee323	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜁 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee323.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee323.2	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
3		ee323.3	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )
4		ee323.4	⊢ ( 𝜃 → ( 𝜏 → ( 𝜂 → 𝜁 ) ) )
5	2	a1dd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
6	1 5 3 4	ee333	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜁 ) ) )