Theorem ee333

Description: e333 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee333.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee333.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
	ee333.3	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )
	ee333.4	⊢ ( 𝜃 → ( 𝜏 → ( 𝜂 → 𝜁 ) ) )
Assertion	ee333	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜁 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee333.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee333.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
3		ee333.3	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )
4		ee333.4	⊢ ( 𝜃 → ( 𝜏 → ( 𝜂 → 𝜁 ) ) )
5	1	3imp	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
6	2	3imp	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜏 )
7	3	3imp	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜂 )
8	5 6 7 4	syl3c	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜁 )
9	8	3exp	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜁 ) ) )