Theorem ee123

Description: e123 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee123.1	⊢ ( 𝜑 → 𝜓 )
	ee123.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
	ee123.3	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
	ee123.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜂 → 𝜁 ) ) )
Assertion	ee123	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜁 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee123.1	⊢ ( 𝜑 → 𝜓 )
2		ee123.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
3		ee123.3	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
4		ee123.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜂 → 𝜁 ) ) )
5	1	a1d	⊢ ( 𝜑 → ( 𝜏 → 𝜓 ) )
6	5	a1d	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜓 ) ) )
7	2	a1dd	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜃 ) ) )
8	6 7 3 4	ee333	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜁 ) ) )