![]() |
Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > frege30 | Structured version Visualization version GIF version |
Description: Commuted, closed form of con3d 152. Proposition 30 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege30 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege29 42177 | . 2 ⊢ ((𝜓 → (𝜑 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) | |
2 | frege10 42166 | . 2 ⊢ (((𝜓 → (𝜑 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) → ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42136 ax-frege2 42137 ax-frege8 42155 ax-frege28 42176 |
This theorem is referenced by: frege59a 42223 frege59b 42250 frege59c 42268 |
Copyright terms: Public domain | W3C validator |