Metamath Proof Explorer


Theorem ee100

Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee100.1 ( 𝜑𝜓 )
ee100.2 𝜒
ee100.3 𝜃
ee100.4 ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) )
Assertion ee100 ( 𝜑𝜏 )

Proof

Step Hyp Ref Expression
1 ee100.1 ( 𝜑𝜓 )
2 ee100.2 𝜒
3 ee100.3 𝜃
4 ee100.4 ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) )
5 2 a1i ( 𝜑𝜒 )
6 3 a1i ( 𝜑𝜃 )
7 1 5 6 4 syl3c ( 𝜑𝜏 )