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Theorem oplem1 931
 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 288 . . . . . 6
3 oplem1.1 . . . . . . 7
43ord 367 . . . . . 6
52, 4syl5bir 210 . . . . 5
6 oplem1.2 . . . . . 6
76ord 367 . . . . 5
85, 7jcad 520 . . . 4
9 oplem1.4 . . . . 5
109biimpar 472 . . . 4
118, 10syl6 31 . . 3
1211pm2.18d 105 . 2
1312, 1sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359 This theorem is referenced by:  preqr1  3964 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361
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