NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  oplem1 Unicode version

Theorem oplem1 930
Description: A specialized lemma for set theory (ordered pair theorem). (Contributed by NM, 18-Oct-1995.) (Proof shortened by Wolf Lammen, 8-Dec-2012.)
Hypotheses
Ref Expression
oplem1.1
oplem1.2
oplem1.3
oplem1.4
Assertion
Ref Expression
oplem1

Proof of Theorem oplem1
StepHypRef Expression
1 oplem1.3 . . . . . . 7
21notbii 287 . . . . . 6
3 oplem1.1 . . . . . . 7
43ord 366 . . . . . 6
52, 4syl5bir 209 . . . . 5
6 oplem1.2 . . . . . 6
76ord 366 . . . . 5
85, 7jcad 519 . . . 4
9 oplem1.4 . . . . 5
109biimpar 471 . . . 4
118, 10syl6 29 . . 3
1211pm2.18d 103 . 2
1312, 1sylibr 203 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
This theorem is referenced by:  preqr1  4124
  Copyright terms: Public domain W3C validator