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Theorem ax12o 1887
 Description: Derive set.mm's original ax-12o 2094 from the shorter ax-12 1878. (Contributed by NM, 29-Nov-2015.) (Revised by NM, 24-Dec-2015.)
Assertion
Ref Expression
ax12o

Proof of Theorem ax12o
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax12v 1879 . . 3
2 ax12v 1879 . . 3
31, 2ax12olem4 1883 . 2
4 ax12v 1879 . . 3
5 ax12v 1879 . . 3
64, 5ax12olem4 1883 . 2
73, 6ax12olem7 1886 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1530 This theorem is referenced by:  ax12  1888  dvelimv  1892  hbae  1906  nfeqf  1911  dvelimh  1917  dvelimf  1950  dvelimALT  2085  ax11eq  2145  ax11indalem  2149  axext4dist  24228  ax12-2  29725  ax12-4  29728  ax10lem17ALT  29745  a12stdy4  29751  a12lem1  29752  ax9lem17  29778 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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