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Mirrors > Home > MPE Home > Th. List > ressnop0 | Structured version Unicode version |
Description: If ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ressnop0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxp1 4972 |
. . 3
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2 | 1 | con3i 135 |
. 2
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3 | df-res 4952 |
. . . 4
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4 | incom 3643 |
. . . 4
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5 | 3, 4 | eqtri 2480 |
. . 3
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6 | disjsn 4036 |
. . . 4
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7 | 6 | biimpri 206 |
. . 3
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8 | 5, 7 | syl5eq 2504 |
. 2
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9 | 2, 8 | syl 16 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4513 ax-nul 4521 ax-pr 4631 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3072 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-nul 3738 df-if 3892 df-sn 3978 df-pr 3980 df-op 3984 df-opab 4451 df-xp 4946 df-res 4952 |
This theorem is referenced by: fvunsn 6011 fsnunres 6020 constr3pthlem1 23678 ex-res 23785 wfrlem14 27873 |
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