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ChopAndNotChopImp

⊢ f ; g ∧¬(f ; g1) ⊃ f ; (g ∧¬g1) ChopAndNotChopImp

Proof:

1
⊢ g ⊃ (g ∧¬g1) ∨ g1
Prop
2
⊢ f ; g ⊃ f ; (g ∧¬g1) ∨ f ; g1
1,LeftChopImpChop
3
⊢ f ; g ∧¬(f ; g1) ⊃ f ; (g ∧¬g1)
2,Prop

qed

Here is a related theorem for the yields operator:

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2023-09-12
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