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Theorem ax10 1677
 Description: Proof of axiom ax-10 1678 from others, without using ax-4 1692, ax-9 1684, or ax-10 1678 but allowing ax-9v 1632. (See remarks for ax12o10lem1 1635 about why we use ax-9v 1632 instead of ax-9 1684.) Our current practice is to use axiom ax-10 1678 from here on instead of theorem ax10 1677, in order to preferentially use ax-9 1684 instead of ax-9v 1632. (Contributed by NM, 25-Jul-2015.) (Revised by NM, 7-Nov-2015.) (New usage is discouraged.)
Assertion
Ref Expression
ax10

Proof of Theorem ax10
StepHypRef Expression
1 ax-9v 1632 . 2
2 df-ex 1538 . . 3
3 ax-17 1628 . . . . 5
4 ax10lem25 1674 . . . . . . . . . 10
54imp 420 . . . . . . . . 9
6 ax10lem23 1672 . . . . . . . . . 10
7 ax12o10lem1 1635 . . . . . . . . . . 11
87alimi 1546 . . . . . . . . . 10
96, 8syl6 31 . . . . . . . . 9
10 ax10lem27 1676 . . . . . . . . 9
115, 9, 10syl56 32 . . . . . . . 8
1211exp3acom23 1368 . . . . . . 7
13 pm2.18 104 . . . . . . 7
1412, 13syl6 31 . . . . . 6
1514com12 29 . . . . 5
163, 15ax10lem18 1667 . . . 4
1716com12 29 . . 3
182, 17syl5bir 211 . 2
191, 18mpi 18 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wa 360  wal 1532  wex 1537 This theorem is referenced by:  e2ebindALT  27396 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-11 1624  ax-17 1628  ax-9v 1632  ax-12 1633 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
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