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Theorem ax12indn 32222
 Description: Induction step for constructing a substitution instance of ax-c15 32169 without using ax-c15 32169. Negation case. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax12indn.1
Assertion
Ref Expression
ax12indn

Proof of Theorem ax12indn
StepHypRef Expression
1 19.8a 1910 . . 3
2 exanali 1717 . . . 4
3 hbn1 1890 . . . . 5
4 hbn1 1890 . . . . 5
5 ax12indn.1 . . . . . . 7
6 con3 139 . . . . . . 7
75, 6syl6 34 . . . . . 6
87com23 81 . . . . 5
93, 4, 8alrimdh 1719 . . . 4
102, 9syl5bi 220 . . 3
111, 10syl5 33 . 2
1211expd 437 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435  wex 1659 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660 This theorem is referenced by:  ax12indi  32223
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