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Theorem oplem1 964
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 296 . . . . . 6
3 oplem1.1 . . . . . . 7
43ord 377 . . . . . 6
52, 4syl5bir 218 . . . . 5
6 oplem1.2 . . . . . 6
76ord 377 . . . . 5
85, 7jcad 533 . . . 4
9 oplem1.4 . . . . 5
109biimpar 485 . . . 4
118, 10syl6 33 . . 3
1211pm2.18d 111 . 2
1312, 1sylibr 212 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369
This theorem is referenced by:  preqr1  4204
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 185  df-or 370  df-an 371
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