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Mirrors > Home > NFE Home > Th. List > r19.2zb | Unicode version |
Description: A response to the notion that the condition can be removed in r19.2z 3639. Interestingly enough, does not figure in the left-hand side. (Contributed by Jeff Hankins, 24-Aug-2009.) |
Ref | Expression |
---|---|
r19.2zb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.2z 3639 | . . 3 | |
2 | 1 | ex 423 | . 2 |
3 | noel 3554 | . . . . . . 7 | |
4 | 3 | pm2.21i 123 | . . . . . 6 |
5 | 4 | rgen 2679 | . . . . 5 |
6 | raleq 2807 | . . . . 5 | |
7 | 5, 6 | mpbiri 224 | . . . 4 |
8 | 7 | necon3bi 2557 | . . 3 |
9 | exsimpl 1592 | . . . 4 | |
10 | df-rex 2620 | . . . 4 | |
11 | n0 3559 | . . . 4 | |
12 | 9, 10, 11 | 3imtr4i 257 | . . 3 |
13 | 8, 12 | ja 153 | . 2 |
14 | 2, 13 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 wne 2516 wral 2614 wrex 2615 c0 3550 |
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-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-nul 3551 |
This theorem is referenced by: (None) |
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