BfImpDist

⊢ (f ⊃ g) ⊃ ( f) ⊃ ( g) BfImpDist

Proof:

1
(f ⊃ g) ⊃ (¬g ⊃ ¬f)
2
¬(¬g ⊃ ¬f) ⊃ ¬(f ⊃ g)
1,Prop
3
(¬(¬g ⊃ ¬f) ⊃ ¬(f ⊃ g))
4
(¬(¬g ⊃ ¬f) ⊃ ¬(f ⊃ g))
⊃ (f ⊃ g) ⊃ (¬g ⊃ ¬f)
5
(f ⊃ g) ⊃ (¬g ⊃ ¬f)
3, 4,MP
6
(¬g ⊃ ¬f) ⊃ ( f) ⊃ ( g)
7
(f ⊃ g) ⊃ ( f) ⊃ ( g)
5, 6,ImpChain

qed

2024-08-03
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