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Mirrors > Home > NFE Home > Th. List > necon3bii | GIF version |
Description: Inference from equality to inequality. (Contributed by NM, 23-Feb-2005.) |
Ref | Expression |
---|---|
necon3bii.1 | ⊢ (A = B ↔ C = D) |
Ref | Expression |
---|---|
necon3bii | ⊢ (A ≠ B ↔ C ≠ D) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon3bii.1 | . . 3 ⊢ (A = B ↔ C = D) | |
2 | 1 | necon3abii 2546 | . 2 ⊢ (A ≠ B ↔ ¬ C = D) |
3 | df-ne 2518 | . 2 ⊢ (C ≠ D ↔ ¬ C = D) | |
4 | 2, 3 | bitr4i 243 | 1 ⊢ (A ≠ B ↔ C ≠ D) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 176 = wceq 1642 ≠ wne 2516 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-ne 2518 |
This theorem is referenced by: necom 2597 nulnnn 4556 rnsnn0 5065 ce2 6192 nchoicelem14 6302 |
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