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Theorem ax11inda2 2276
 Description: Induction step for constructing a substitution instance of ax-11o 2218 without using ax-11o 2218. Quantification case. When and are distinct, this theorem avoids the dummy variables needed by the more general ax11inda 2277. (Contributed by NM, 24-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11inda2.1
Assertion
Ref Expression
ax11inda2
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem ax11inda2
StepHypRef Expression
1 ax-1 5 . . . . 5
2 a16g-o 2263 . . . . 5
31, 2syl5 30 . . . 4
43a1d 23 . . 3
54a1d 23 . 2
6 ax11inda2.1 . . 3
76ax11indalem 2274 . 2
85, 7pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  ax11inda  2277 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-4 2212  ax-5o 2213  ax-6o 2214  ax-10o 2216  ax-12o 2219  ax-16 2221 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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