Metamath Proof Explorer


Theorem ee211

Description: e211 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee211.1 ( 𝜑 → ( 𝜓𝜒 ) )
ee211.2 ( 𝜑𝜃 )
ee211.3 ( 𝜑𝜏 )
ee211.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
Assertion ee211 ( 𝜑 → ( 𝜓𝜂 ) )

Proof

Step Hyp Ref Expression
1 ee211.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 ee211.2 ( 𝜑𝜃 )
3 ee211.3 ( 𝜑𝜏 )
4 ee211.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 2 a1d ( 𝜑 → ( 𝜓𝜃 ) )
6 3 a1d ( 𝜑 → ( 𝜓𝜏 ) )
7 1 5 6 4 ee222 ( 𝜑 → ( 𝜓𝜂 ) )