Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax11o Unicode version

Theorem ax11o 2047
 Description: Derivation of set.mm's original ax-11o 2191 from ax-10 2190 and the shorter ax-11 1757 that has replaced it. An open problem is whether this theorem can be proved without relying on ax-16 2194 or ax-17 1623 (given all of the original and new versions of sp 1759 through ax-15 2193). Another open problem is whether this theorem can be proved without relying on ax12o 1976. Theorem ax11 2205 shows the reverse derivation of ax-11 1757 from ax-11o 2191. Normally, ax11o 2047 should be used rather than ax-11o 2191, except by theorems specifically studying the latter's properties. (Contributed by NM, 3-Feb-2007.)
Assertion
Ref Expression
ax11o

Proof of Theorem ax11o
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-11 1757 . 2
21ax11a2 2046 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1546 This theorem is referenced by:  ax11b  2048  equs5  2049  ax11v  2145 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-tru 1325  df-ex 1548  df-nf 1551
 Copyright terms: Public domain W3C validator