Theorem ee112

Description: e112 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee112.1	⊢ ( 𝜑 → 𝜓 )
	ee112.2	⊢ ( 𝜑 → 𝜒 )
	ee112.3	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
	ee112.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee112	⊢ ( 𝜑 → ( 𝜃 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee112.1	⊢ ( 𝜑 → 𝜓 )
2		ee112.2	⊢ ( 𝜑 → 𝜒 )
3		ee112.3	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
4		ee112.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5	1	a1d	⊢ ( 𝜑 → ( 𝜃 → 𝜓 ) )
6	2	a1d	⊢ ( 𝜑 → ( 𝜃 → 𝜒 ) )
7	5 6 3 4	ee222	⊢ ( 𝜑 → ( 𝜃 → 𝜂 ) )