Theorem ee122

Description: e122 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee122.1	⊢ ( 𝜑 → 𝜓 )
	ee122.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
	ee122.3	⊢ ( 𝜑 → ( 𝜒 → 𝜏 ) )
	ee122.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee122	⊢ ( 𝜑 → ( 𝜒 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee122.1	⊢ ( 𝜑 → 𝜓 )
2		ee122.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
3		ee122.3	⊢ ( 𝜑 → ( 𝜒 → 𝜏 ) )
4		ee122.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	a1d	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )
6	5 2 3 4	ee222	⊢ ( 𝜑 → ( 𝜒 → 𝜂 ) )