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Theorem bj-axemptylem 13427
 Description: Lemma for bj-axempty 13428 and bj-axempty2 13429. (Contributed by BJ, 25-Oct-2020.) (Proof modification is discouraged.) Use ax-nul 4090 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 13368 . . 3 BOUNDED
21bdsep1 13420 . 2
3 biimp 117 . . . 4
4 falimd 1350 . . . 4
53, 4syl6 33 . . 3
65alimi 1435 . 2
72, 6eximii 1582 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1333   wfal 1340  wex 1472 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 604  ax-in2 605  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514  ax-bd0 13348  ax-bdim 13349  ax-bdn 13352  ax-bdeq 13355  ax-bdsep 13419 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341 This theorem is referenced by:  bj-axempty  13428  bj-axempty2  13429
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