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Theorem ax11indn 2245
 Description: Induction step for constructing a substitution instance of ax-11o 2191 without using ax-11o 2191. Negation case. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11indn.1
Assertion
Ref Expression
ax11indn

Proof of Theorem ax11indn
StepHypRef Expression
1 19.8a 1758 . . 3
2 exanali 1592 . . . 4
3 hbn1 1741 . . . . 5
4 hbn1 1741 . . . . 5
5 ax11indn.1 . . . . . . 7
6 con3 128 . . . . . . 7
75, 6syl6 31 . . . . . 6
87com23 74 . . . . 5
93, 4, 8alrimdh 1594 . . . 4
102, 9syl5bi 209 . . 3
111, 10syl5 30 . 2
1211exp3a 426 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1546  wex 1547 This theorem is referenced by:  ax11indi  2246 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548
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