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Theorem ax12inda2 2277
 Description: Induction step for constructing a substitution instance of ax-c15 2220 without using ax-c15 2220. Quantification case. When and are distinct, this theorem avoids the dummy variables needed by the more general ax12inda 2278. (Contributed by NM, 24-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax12inda2.1
Assertion
Ref Expression
ax12inda2
Distinct variable group:   ,

Proof of Theorem ax12inda2
StepHypRef Expression
1 ax-1 6 . . . . 5
2 ax16g-o 2264 . . . . 5
31, 2syl5 32 . . . 4
43a1d 25 . . 3
54a1d 25 . 2
6 ax12inda2.1 . . 3
76ax12indalem 2275 . 2
85, 7pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  A.wal 1393 This theorem is referenced by:  ax12inda  2278 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-11 1842  ax-12 1854  ax-13 1999  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221  ax-c16 2223 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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