Metamath Proof Explorer


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 → ( 𝜓𝜒 ) )
ee221.2 ( 𝜑 → ( 𝜓𝜃 ) )
ee221.3 ( 𝜑𝜏 )
ee221.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
Assertion ee221 ( 𝜑 → ( 𝜓𝜂 ) )

Proof

Step Hyp Ref Expression
1 ee221.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 ee221.2 ( 𝜑 → ( 𝜓𝜃 ) )
3 ee221.3 ( 𝜑𝜏 )
4 ee221.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 3 a1d ( 𝜑 → ( 𝜓𝜏 ) )
6 1 2 5 4 ee222 ( 𝜑 → ( 𝜓𝜂 ) )