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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-axemptylem | Unicode version |
Description: Lemma for bj-axempty 13091 and bj-axempty2 13092. (Contributed by BJ, 25-Oct-2020.) (Proof modification is discouraged.) Use ax-nul 4054 instead. (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-axemptylem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdfal 13031 | . . 3 BOUNDED | |
2 | 1 | bdsep1 13083 | . 2 |
3 | bi1 117 | . . . 4 | |
4 | falimd 1346 | . . . 4 | |
5 | 3, 4 | syl6 33 | . . 3 |
6 | 5 | alimi 1431 | . 2 |
7 | 2, 6 | eximii 1581 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wfal 1336 wex 1468 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-ial 1514 ax-bd0 13011 ax-bdim 13012 ax-bdn 13015 ax-bdeq 13018 ax-bdsep 13082 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 |
This theorem is referenced by: bj-axempty 13091 bj-axempty2 13092 |
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