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Theorem ax12indn 2273
Description: Induction step for constructing a substitution instance of ax-c15 2220 without using ax-c15 2220. 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 1857 . . 3
2 exanali 1670 . . . 4
3 hbn1 1838 . . . . 5
4 hbn1 1838 . . . . 5
5 ax12indn.1 . . . . . . 7
6 con3 134 . . . . . . 7
75, 6syl6 33 . . . . . 6
87com23 78 . . . . 5
93, 4, 8alrimdh 1672 . . . 4
102, 9syl5bi 217 . . 3
111, 10syl5 32 . 2
1211expd 436 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
This theorem is referenced by:  ax12indi  2274
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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