Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax12o Unicode version

Theorem ax12o 1976
 Description: Derive set.mm's original ax-12o 2190 from the shorter ax-12 1946. (Contributed by NM, 29-Nov-2015.) (Revised by NM, 24-Dec-2015.) (Revised by Wolf Lammen, 30-Jan-2018.)
Assertion
Ref Expression
ax12o

Proof of Theorem ax12o
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax12v 1947 . . 3
2 ax12v 1947 . . 3
31, 2ax12olem3 1974 . 2
4 ax12v 1947 . . 3
5 ax12v 1947 . . 3
64, 5ax12olem3 1974 . 2
73, 6ax12olem4 1975 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1546 This theorem is referenced by:  ax12  1985  ax12OLD  1986  dvelimvOLD  1994  hbae  2005  nfeqf  2014  dvelimhOLD  2016  dvelimf  2048  dvelimALT  2181  ax11eq  2241  ax11indalem  2245  axi12  2381  axext4dist  25340 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
 Copyright terms: Public domain W3C validator