Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax9OLD Structured version   Unicode version

Theorem ax9OLD 2034
 Description: Obsolete proof of ax9 1954 as of 4-Feb-2018. (Contributed by NM, 12-Nov-2013.) (Revised by NM, 25-Jul-2015.) (New usage is discouraged.) (Proof modfication is discouraged.)
Assertion
Ref Expression
ax9OLD

Proof of Theorem ax9OLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sp 1764 . . 3
2 sp 1764 . . 3
31, 2nsyl3 114 . 2
4 ax9v 1668 . . 3
5 dveeq2OLD 2030 . . . . . 6
6 ax9v 1668 . . . . . . 7
7 hba1 1805 . . . . . . . 8
8 equequ2 1699 . . . . . . . . . 10
98sps 1771 . . . . . . . . 9
109notbid 287 . . . . . . . 8
117, 10albidh 1601 . . . . . . 7
126, 11mtbii 295 . . . . . 6
135, 12syl6com 34 . . . . 5
1413con3i 130 . . . 4
1514alrimiv 1642 . . 3
164, 15mt3 174 . 2
173, 16pm2.61i 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
 Copyright terms: Public domain W3C validator