Metamath Proof Explorer


Theorem ee30

Description: e30 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee30.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
ee30.2 𝜏
ee30.3 ( 𝜃 → ( 𝜏𝜂 ) )
Assertion ee30 ( 𝜑 → ( 𝜓 → ( 𝜒𝜂 ) ) )

Proof

Step Hyp Ref Expression
1 ee30.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
2 ee30.2 𝜏
3 ee30.3 ( 𝜃 → ( 𝜏𝜂 ) )
4 2 a1i ( 𝜒𝜏 )
5 4 a1i ( 𝜓 → ( 𝜒𝜏 ) )
6 5 a1i ( 𝜑 → ( 𝜓 → ( 𝜒𝜏 ) ) )
7 1 6 3 ee33 ( 𝜑 → ( 𝜓 → ( 𝜒𝜂 ) ) )