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Theorem ax10 1944
 Description: Derive set.mm's original ax-10 2140 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 1655 . 2
2 df-ex 1542 . . 3
3 dveeq2 1940 . . . . . . . 8
43imp 418 . . . . . . 7
5 ax10lem6 1943 . . . . . . . 8
6 equcomi 1679 . . . . . . . . 9
76alimi 1559 . . . . . . . 8
85, 7syl6 29 . . . . . . 7
9 ax10lem5 1942 . . . . . . 7
104, 8, 9syl56 30 . . . . . 6
1110exp3acom23 1372 . . . . 5
12 pm2.18 102 . . . . 5
1311, 12syl6 29 . . . 4
1413exlimdv 1636 . . 3
152, 14syl5bir 209 . 2
161, 15mpi 16 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540  wex 1541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  aecom  1946  ax10o  1952  axi10  2331
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