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Theorem ax9X 28232
 Description: Theorem showing that ax-9 1684 follows from the weaker version ax-9v 1632. This theorem normally should not be referenced in any later proof. Instead, the use of ax-9 1684 below is preferred, since it is easier to work with (it has no distinct variable conditions) and it is the standard version we have adopted. (Contributed by NM, 12-Nov-2013.) (Revised by NM, 25-Jul-2015.) (New usage is discouraged.)
Assertion
Ref Expression
ax9X

Proof of Theorem ax9X
StepHypRef Expression
1 ax12o10lem3 1637 . . 3
2 ax12o10lem3 1637 . . 3
31, 2nsyl3 113 . 2
4 ax-9v 1632 . . 3
5 ax-17 1628 . . . 4
6 ax10lem25 1674 . . . . . 6
7 ax-9v 1632 . . . . . . 7
8 ax12o10lem5 1639 . . . . . . . 8
9 ax12o10lem3 1637 . . . . . . . . . 10
10 ax10lem16 1665 . . . . . . . . . 10
119, 10syl 17 . . . . . . . . 9
1211notbid 287 . . . . . . . 8
138, 12albidh 1589 . . . . . . 7
147, 13mtbii 295 . . . . . 6
156, 14syl6com 33 . . . . 5
1615con3i 129 . . . 4
175, 16alrimih 1553 . . 3
184, 17mt3 173 . 2
193, 18pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178  wal 1532 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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