Metamath Proof Explorer


Theorem ee22an

Description: e22an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee22an.1 ( 𝜑 → ( 𝜓𝜒 ) )
ee22an.2 ( 𝜑 → ( 𝜓𝜃 ) )
ee22an.3 ( ( 𝜒𝜃 ) → 𝜏 )
Assertion ee22an ( 𝜑 → ( 𝜓𝜏 ) )

Proof

Step Hyp Ref Expression
1 ee22an.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 ee22an.2 ( 𝜑 → ( 𝜓𝜃 ) )
3 ee22an.3 ( ( 𝜒𝜃 ) → 𝜏 )
4 3 ex ( 𝜒 → ( 𝜃𝜏 ) )
5 1 2 4 syl6c ( 𝜑 → ( 𝜓𝜏 ) )