New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > necom | GIF version |
Description: Commutation of inequality. (Contributed by NM, 14-May-1999.) |
Ref | Expression |
---|---|
necom | ⊢ (A ≠ B ↔ B ≠ A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2355 | . 2 ⊢ (A = B ↔ B = A) | |
2 | 1 | necon3bii 2548 | 1 ⊢ (A ≠ B ↔ B ≠ A) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ≠ wne 2516 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-cleq 2346 df-ne 2518 |
This theorem is referenced by: necomi 2598 necomd 2599 0pss 3588 difprsn1 3847 difprsn2 3848 diftpsn3 3849 fvpr1 5449 fvpr2 5450 |
Copyright terms: Public domain | W3C validator |