![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > con1biddc | GIF version |
Description: A contraposition deduction. (Contributed by Jim Kingdon, 4-Apr-2018.) |
Ref | Expression |
---|---|
con1biddc.1 | ⊢ (𝜑 → (DECID 𝜓 → (¬ 𝜓 ↔ 𝜒))) |
Ref | Expression |
---|---|
con1biddc | ⊢ (𝜑 → (DECID 𝜓 → (¬ 𝜒 ↔ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con1biddc.1 | . 2 ⊢ (𝜑 → (DECID 𝜓 → (¬ 𝜓 ↔ 𝜒))) | |
2 | con1biimdc 874 | . 2 ⊢ (DECID 𝜓 → ((¬ 𝜓 ↔ 𝜒) → (¬ 𝜒 ↔ 𝜓))) | |
3 | 1, 2 | sylcom 28 | 1 ⊢ (𝜑 → (DECID 𝜓 → (¬ 𝜒 ↔ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 105 DECID wdc 835 |
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 615 ax-in2 616 ax-io 710 |
This theorem depends on definitions: df-bi 117 df-stab 832 df-dc 836 |
This theorem is referenced by: con2biddc 881 pm5.18dc 884 necon1abiddc 2419 necon1bbiddc 2420 |
Copyright terms: Public domain | W3C validator |