![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > pm2.521dcALT | GIF version |
Description: Alternate proof of pm2.521dc 869. (Contributed by Jim Kingdon, 5-May-2018.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pm2.521dcALT | ⊢ (DECID 𝜑 → (¬ (𝜑 → 𝜓) → (𝜓 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.52 656 | . 2 ⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → ¬ 𝜓)) | |
2 | condc 853 | . 2 ⊢ (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑))) | |
3 | 1, 2 | syl5 32 | 1 ⊢ (DECID 𝜑 → (¬ (𝜑 → 𝜓) → (𝜓 → 𝜑))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 DECID wdc 834 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-stab 831 df-dc 835 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |