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Theorem bj-axemptylem 10012
 Description: Lemma for bj-axempty 10013 and bj-axempty2 10014. (Contributed by BJ, 25-Oct-2020.) (Proof modification is discouraged.) Use ax-nul 3883 instead. (New usage is discouraged.)
Assertion
Ref Expression
bj-axemptylem
Distinct variable group:   ,

Proof of Theorem bj-axemptylem
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdfal 9953 . . 3 BOUNDED
21bdsep1 10005 . 2
3 bi1 111 . . . 4
4 falimd 1258 . . . 4
53, 4syl6 29 . . 3
65alimi 1344 . 2
72, 6eximii 1493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wfal 1248  wex 1381 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 This theorem is referenced by:  bj-axempty  10013  bj-axempty2  10014
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