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Theorem ax11inda 2113
 Description: Induction step for constructing a substitution instance of ax-11o 1940 without using ax-11o 1940. Quantification case. (When and are distinct, ax11inda2 2112 may be used instead to avoid the dummy variable in the proof.) (Contributed by NM, 24-Jan-2007.)
Hypothesis
Ref Expression
ax11inda.1
Assertion
Ref Expression
ax11inda
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem ax11inda
StepHypRef Expression
1 a9e 1817 . . 3
2 ax11inda.1 . . . . . . 7
32ax11inda2 2112 . . . . . 6
4 dveeq2-o 1929 . . . . . . . . 9
54imp 420 . . . . . . . 8
6 hba1 1718 . . . . . . . . . 10
7 equequ2 1830 . . . . . . . . . . 11
87a4s 1700 . . . . . . . . . 10
96, 8albidh 1589 . . . . . . . . 9
109notbid 287 . . . . . . . 8
115, 10syl 17 . . . . . . 7
127adantl 454 . . . . . . . 8
138imbi1d 310 . . . . . . . . . . 11
146, 13albidh 1589 . . . . . . . . . 10
155, 14syl 17 . . . . . . . . 9
1615imbi2d 309 . . . . . . . 8
1712, 16imbi12d 313 . . . . . . 7
1811, 17imbi12d 313 . . . . . 6
193, 18mpbii 204 . . . . 5
2019ex 425 . . . 4
2120exlimdv 1932 . . 3
221, 21mpi 18 . 2
2322pm2.43i 45 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wa 360  wal 1532  wex 1537 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-17 1628  ax-12o 1664  ax-9 1684  ax-4 1692  ax-10o 1835  ax-16 1926 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540
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