Metamath Proof Explorer


Theorem ee03

Description: e03 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee03.1 𝜑
ee03.2 ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) )
ee03.3 ( 𝜑 → ( 𝜏𝜂 ) )
Assertion ee03 ( 𝜓 → ( 𝜒 → ( 𝜃𝜂 ) ) )

Proof

Step Hyp Ref Expression
1 ee03.1 𝜑
2 ee03.2 ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) )
3 ee03.3 ( 𝜑 → ( 𝜏𝜂 ) )
4 1 a1i ( 𝜓𝜑 )
5 4 a1d ( 𝜓 → ( 𝜒𝜑 ) )
6 5 a1dd ( 𝜓 → ( 𝜒 → ( 𝜃𝜑 ) ) )
7 6 2 3 ee33 ( 𝜓 → ( 𝜒 → ( 𝜃𝜂 ) ) )