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Theorem ax11indn 1813
Description: Induction step for constructing a substitution instance of ax-11o 1654 without using ax-11o 1654. Negation case.
Hypothesis
Ref Expression
ax11indn.1
Assertion
Ref Expression
ax11indn

Proof of Theorem ax11indn
StepHypRef Expression
1 19.8a 1479 . . 3
2 exanali 1508 . . . 4
3 hbn1 1448 . . . . 5
4 hbn1 1448 . . . . 5
5 ax11indn.1 . . . . . . 7
6 con3 550 . . . . . . 7
75, 6syl6 28 . . . . . 6
87com23 71 . . . . 5
93, 4, 8alrimd 1359 . . . 4
102, 9syl5bi 140 . . 3
111, 10syl5 27 . 2
1211exp3a 244 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 96  wal 1335  wex 1374
This theorem is referenced by:  ax11indi  1814  a12studyALT  1826
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100  ax-in1 527  ax-in2 528  ax-5 1336  ax-6 1337  ax-gen 1339  ax-ie1 1375  ax-ie2 1376  ax-4 1392  ax-ial 1430
This theorem depends on definitions:  df-bi 109  df-tru 1313  df-fal 1314
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