Metamath Proof Explorer


Theorem ee202

Description: e202 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee202.1 ( 𝜑 → ( 𝜓𝜒 ) )
ee202.2 𝜃
ee202.3 ( 𝜑 → ( 𝜓𝜏 ) )
ee202.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
Assertion ee202 ( 𝜑 → ( 𝜓𝜂 ) )

Proof

Step Hyp Ref Expression
1 ee202.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 ee202.2 𝜃
3 ee202.3 ( 𝜑 → ( 𝜓𝜏 ) )
4 ee202.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 2 a1i ( 𝜓𝜃 )
6 5 a1i ( 𝜑 → ( 𝜓𝜃 ) )
7 1 6 3 4 ee222 ( 𝜑 → ( 𝜓𝜂 ) )