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Theorem ax12o 1663
 Description: Derive set.mm's original ax-12o 1664 from the shorter ax-12 1633. Our current practice is to use axiom ax-12o 1664 from here on (except in the proofs of ax10 1677 and ax9 1683 below) instead of theorem ax12o 1663 in order to standardize the use ax-9 1684 instead of ax-9v 1632. Note that the derivation of ax-9 1684 from ax-9v 1632 (theorem ax9 1683 below) makes use of ax12o 1663; thus we use ax-9v 1632 to prove ax12o 1663 to avoid a circular argument . (Contributed by NM, 29-Nov-2015.) (Revised by NM, 24-Dec-2015.) (New usage is discouraged.)
Assertion
Ref Expression
ax12o

Proof of Theorem ax12o
StepHypRef Expression
1 ax12v 1634 . . 3
2 ax12v 1634 . . 3
31, 2ax12olem24 1658 . 2
4 ax12v 1634 . . 3
5 ax12v 1634 . . 3
64, 5ax12olem24 1658 . 2
73, 6ax12olem28 1662 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6  wal 1532 This theorem is referenced by:  ax10lem24  1673 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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