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Mirrors > Home > NFE Home > Th. List > necon3abii | GIF version |
Description: Deduction from equality to inequality. (Contributed by NM, 9-Nov-2007.) |
Ref | Expression |
---|---|
necon3abii.1 | ⊢ (A = B ↔ φ) |
Ref | Expression |
---|---|
necon3abii | ⊢ (A ≠ B ↔ ¬ φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2518 | . 2 ⊢ (A ≠ B ↔ ¬ A = B) | |
2 | necon3abii.1 | . 2 ⊢ (A = B ↔ φ) | |
3 | 1, 2 | xchbinx 301 | 1 ⊢ (A ≠ B ↔ ¬ φ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 176 = wceq 1642 ≠ wne 2516 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-ne 2518 |
This theorem is referenced by: necon3bbii 2547 necon3bii 2548 necompl 3544 n0f 3558 foconst 5280 |
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