Theorem ee221

Description: e221 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee221.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee221.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
	ee221.3	⊢ ( 𝜑 → 𝜏 )
	ee221.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee221	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee221.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee221.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
3		ee221.3	⊢ ( 𝜑 → 𝜏 )
4		ee221.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	3	a1d	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
6	1 2 5 4	ee222	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )