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Mirrors > Home > ILE Home > Th. List > equidqe | Unicode version |
Description: equid 1589 with some quantification and negation without using ax-4 1400 or ax-17 1419. (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 27-Feb-2014.) |
Ref | Expression |
---|---|
equidqe |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-9 1424 | . 2 | |
2 | ax-8 1395 | . . . . 5 | |
3 | 2 | pm2.43i 43 | . . . 4 |
4 | 3 | con3i 562 | . . 3 |
5 | 4 | alimi 1344 | . 2 |
6 | 1, 5 | mto 588 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wal 1241 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1336 ax-gen 1338 ax-ie2 1383 ax-8 1395 ax-i9 1423 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 |
This theorem is referenced by: ax4sp1 1426 |
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