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Theorem ax10 1897
 Description: Derive set.mm's original ax-10 2092 from others. (Contributed by NM, 25-Jul-2015.) (Revised by NM, 7-Nov-2015.)
Assertion
Ref Expression
ax10

Proof of Theorem ax10
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax9v 1645 . 2
2 df-ex 1532 . . 3
3 dveeq2 1893 . . . . . . . 8
43imp 418 . . . . . . 7
5 ax10lem6 1896 . . . . . . . 8
6 equcomi 1664 . . . . . . . . 9
76alimi 1549 . . . . . . . 8
85, 7syl6 29 . . . . . . 7
9 ax10lem5 1895 . . . . . . 7
104, 8, 9syl56 30 . . . . . 6
1110exp3acom23 1362 . . . . 5
12 pm2.18 102 . . . . 5
1311, 12syl6 29 . . . 4
1413exlimdv 1626 . . 3
152, 14syl5bir 209 . 2
161, 15mpi 16 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1530  wex 1531 This theorem is referenced by:  aecom  1899  ax10o  1905  2sb5ndVD  29002  e2ebindVD  29004  e2ebindALT  29022  2sb5ndALT  29025 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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