New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  ax12olem6 Unicode version

Theorem ax12olem6 1932
 Description: Lemma for ax12o 1934. Derivation of ax12o 1934 from the hypotheses, without using ax12o 1934. (Contributed by Andrew Salmon, 21-Jul-2011.) (Revised by NM, 24-Dec-2015.)
Hypotheses
Ref Expression
ax12olem6.1
ax12olem6.2
Assertion
Ref Expression
ax12olem6
Distinct variable groups:   ,   ,   ,

Proof of Theorem ax12olem6
StepHypRef Expression
1 hbn1 1730 . . . . 5
2 ax12olem6.1 . . . . 5
31, 2hbim1 1810 . . . 4
4 ax-17 1616 . . . 4
5 equcom 1680 . . . . . 6
6 equequ1 1684 . . . . . 6
75, 6syl5bb 248 . . . . 5
87imbi2d 307 . . . 4
9 ax12olem6.2 . . . 4
103, 4, 8, 9dvelimhw 1849 . . 3
11119.21h 1797 . . 3
1210, 11syl6ib 217 . 2
1312pm2.86d 93 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax12olem7  1933
 Copyright terms: Public domain W3C validator