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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-notbid | GIF version |
Description: Deduction form of bj-notbi 10716. (Contributed by BJ, 27-Jan-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-notbid.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
bj-notbid | ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-notbid.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | bj-notbi 10716 | . 2 ⊢ ((𝜓 ↔ 𝜒) → (¬ 𝜓 ↔ ¬ 𝜒)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ 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) |
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