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Mirrors > Home > MPE Home > Th. List > opabn0 | Structured version Visualization version Unicode version |
Description: Nonempty ordered pair class abstraction. (Contributed by NM, 10-Oct-2007.) |
Ref | Expression |
---|---|
opabn0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0 3709 |
. 2
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2 | elopab 4682 |
. . . 4
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3 | 2 | exbii 1722 |
. . 3
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4 | exrot3 1935 |
. . . 4
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5 | opex 4637 |
. . . . . . 7
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6 | 5 | isseti 3019 |
. . . . . 6
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7 | 19.41v 1834 |
. . . . . 6
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8 | 6, 7 | mpbiran 929 |
. . . . 5
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9 | 8 | 2exbii 1723 |
. . . 4
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10 | 4, 9 | bitri 257 |
. . 3
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11 | 3, 10 | bitri 257 |
. 2
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12 | 1, 11 | bitri 257 |
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 ax-gen 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-v 3015 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-sn 3937 df-pr 3939 df-op 3943 df-opab 4434 |
This theorem is referenced by: csbopab 4706 dvdsrval 17884 thlle 19271 bcthlem5 22307 lgsquadlem3 24296 |
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