Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax11v2 Unicode version

Theorem ax11v2 2045
 Description: Recovery of ax-11o 2191 from ax11v 2145. This proof uses ax-10 2190 and ax-11 1757. TODO: figure out if this is useful, or if it should be simplified or eliminated. (Contributed by NM, 2-Feb-2007.)
Hypothesis
Ref Expression
ax11v2.1
Assertion
Ref Expression
ax11v2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11v2
StepHypRef Expression
1 a9ev 1664 . 2
2 ax11v2.1 . . . . 5
3 equequ2 1694 . . . . . . 7
43adantl 453 . . . . . 6
5 dveeq2 2019 . . . . . . . . 9
65imp 419 . . . . . . . 8
7 nfa1 1802 . . . . . . . . 9
83imbi1d 309 . . . . . . . . . 10
98sps 1766 . . . . . . . . 9
107, 9albid 1784 . . . . . . . 8
116, 10syl 16 . . . . . . 7
1211imbi2d 308 . . . . . 6
134, 12imbi12d 312 . . . . 5
142, 13mpbii 203 . . . 4
1514ex 424 . . 3
1615exlimdv 1643 . 2
171, 16mpi 17 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1546  wex 1547 This theorem is referenced by:  ax11a2  2046 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