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Mirrors > Home > NFE Home > Th. List > oplem1 | Unicode version |
Description: A specialized lemma for set theory (ordered pair theorem). (Contributed by NM, 18-Oct-1995.) (Proof shortened by Wolf Lammen, 8-Dec-2012.) |
Ref | Expression |
---|---|
oplem1.1 |
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oplem1.2 |
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oplem1.3 |
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oplem1.4 |
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Ref | Expression |
---|---|
oplem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oplem1.3 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | notbii 287 |
. . . . . 6
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3 | oplem1.1 |
. . . . . . 7
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4 | 3 | ord 366 |
. . . . . 6
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5 | 2, 4 | syl5bir 209 |
. . . . 5
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6 | oplem1.2 |
. . . . . 6
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7 | 6 | ord 366 |
. . . . 5
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8 | 5, 7 | jcad 519 |
. . . 4
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9 | oplem1.4 |
. . . . 5
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10 | 9 | biimpar 471 |
. . . 4
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11 | 8, 10 | syl6 29 |
. . 3
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12 | 11 | pm2.18d 103 |
. 2
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13 | 12, 1 | sylibr 203 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 4125 |
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