Metamath Proof Explorer


Theorem ee03an

Description: Conjunction form of ee03 . (Contributed by Alan Sare, 18-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee03an.1 𝜑
ee03an.2 ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) )
ee03an.3 ( ( 𝜑𝜏 ) → 𝜂 )
Assertion ee03an ( 𝜓 → ( 𝜒 → ( 𝜃𝜂 ) ) )

Proof

Step Hyp Ref Expression
1 ee03an.1 𝜑
2 ee03an.2 ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) )
3 ee03an.3 ( ( 𝜑𝜏 ) → 𝜂 )
4 3 ex ( 𝜑 → ( 𝜏𝜂 ) )
5 1 2 4 ee03 ( 𝜓 → ( 𝜒 → ( 𝜃𝜂 ) ) )