Theorem ee212

Description: e212 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee212.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee212.2	⊢ ( 𝜑 → 𝜃 )
	ee212.3	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
	ee212.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee212	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee212.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee212.2	⊢ ( 𝜑 → 𝜃 )
3		ee212.3	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
4		ee212.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	a1d	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
6	1 5 3 4	ee222	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )