Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-notbii | GIF version |
Description: Inference associated with bj-notbi 10716. (Contributed by BJ, 27-Jan-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-notbii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
bj-notbii | ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-notbii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
2 | bj-notbi 10716 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (¬ 𝜑 ↔ ¬ 𝜓)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |