Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  a12peros Unicode version

Theorem a12peros 29743
 Description: Experiment to study ax12o 1887. (Contributed by NM, 9-Dec-1015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
a12study10.p
a12study10.q
a12study10.r
a12study10.s
a12study10.t
Assertion
Ref Expression
a12peros
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,,)   (,,)

Proof of Theorem a12peros
StepHypRef Expression
1 a12study10.p . . 3
2 a12study8 29741 . . . 4
3 a12study10.s . . . . . 6
4 exnal 1564 . . . . . . 7
54imbi1i 315 . . . . . 6
63, 5bitr2i 241 . . . . 5
7 a12study10.r . . . . . 6
8 df-ex 1532 . . . . . . . 8
98imbi1i 315 . . . . . . 7
109imbi2i 303 . . . . . 6
117, 10bitr2i 241 . . . . 5
126, 11orbi12i 507 . . . 4
132, 12bitri 240 . . 3
141, 13bitri 240 . 2
15 orcom 376 . 2
1614, 15bitri 240 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wo 357  wal 1530  wex 1531 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1532
 Copyright terms: Public domain W3C validator