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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-axempty | Unicode version |
Description: Axiom of the empty set from bounded separation. It is provable from bounded separation since the intuitionistic FOL used in iset.mm assumes a non-empty universe. See axnul 3882. (Contributed by BJ, 25-Oct-2020.) (Proof modification is discouraged.) Use ax-nul 3883 instead. (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-axempty |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-axemptylem 10012 | . 2 | |
2 | df-ral 2311 | . . 3 | |
3 | 2 | exbii 1496 | . 2 |
4 | 1, 3 | mpbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wfal 1248 wex 1381 wral 2306 |
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-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 ax-bd0 9933 ax-bdim 9934 ax-bdn 9937 ax-bdeq 9940 ax-bdsep 10004 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-ral 2311 |
This theorem is referenced by: (None) |
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