Metamath Proof Explorer


Theorem ee120

Description: Virtual deduction rule e120 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee120.1 ( 𝜑𝜓 )
ee120.2 ( 𝜑 → ( 𝜒𝜃 ) )
ee120.3 𝜏
ee120.4 ( 𝜓 → ( 𝜃 → ( 𝜏𝜂 ) ) )
Assertion ee120 ( 𝜑 → ( 𝜒𝜂 ) )

Proof

Step Hyp Ref Expression
1 ee120.1 ( 𝜑𝜓 )
2 ee120.2 ( 𝜑 → ( 𝜒𝜃 ) )
3 ee120.3 𝜏
4 ee120.4 ( 𝜓 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 1 a1d ( 𝜑 → ( 𝜒𝜓 ) )
6 3 a1i ( 𝜒𝜏 )
7 6 a1i ( 𝜑 → ( 𝜒𝜏 ) )
8 5 2 7 4 ee222 ( 𝜑 → ( 𝜒𝜂 ) )