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Theorem ax11indn 2108
 Description: Induction step for constructing a substitution instance of ax-11o 1940 without using ax-11o 1940. Negation case. (Contributed by NM, 21-Jan-2007.)
Hypothesis
Ref Expression
ax11indn.1
Assertion
Ref Expression
ax11indn

Proof of Theorem ax11indn
StepHypRef Expression
1 19.8a 1758 . . 3
2 exanali 1583 . . . 4
3 hbn1 1564 . . . . 5
4 hbn1 1564 . . . . 5
5 ax11indn.1 . . . . . . 7
6 con3 128 . . . . . . 7
75, 6syl6 31 . . . . . 6
87com23 74 . . . . 5
93, 4, 8alrimdh 1585 . . . 4
102, 9syl5bi 210 . . 3
111, 10syl5 30 . 2
1211exp3a 427 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wa 360  wal 1532  wex 1537 This theorem is referenced by:  ax11indi  2109 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
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