New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > pm2.61dne | Unicode version |
Description: Deduction eliminating an inequality in an antecedent. (Contributed by NM, 1-Jun-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
pm2.61dne.1 | |
pm2.61dne.2 |
Ref | Expression |
---|---|
pm2.61dne |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61dne.2 | . 2 | |
2 | nne 2520 | . . 3 | |
3 | pm2.61dne.1 | . . 3 | |
4 | 2, 3 | syl5bi 208 | . 2 |
5 | 1, 4 | pm2.61d 150 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 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: pm2.61dane 2594 |
Copyright terms: Public domain | W3C validator |