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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > difres | Structured version Visualization version Unicode version |
Description: Case when class difference in unaffected by restriction. (Contributed by Thierry Arnoux, 1-Jan-2020.) |
Ref | Expression |
---|---|
difres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 4865 |
. . 3
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2 | 1 | difeq2i 3560 |
. 2
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3 | difindi 3709 |
. . . 4
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4 | ssdif 3580 |
. . . . . . 7
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5 | difid 3847 |
. . . . . . 7
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6 | 4, 5 | syl6sseq 3490 |
. . . . . 6
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7 | ss0 3777 |
. . . . . 6
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8 | 6, 7 | syl 17 |
. . . . 5
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9 | 8 | uneq2d 3600 |
. . . 4
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10 | 3, 9 | syl5eq 2508 |
. . 3
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11 | un0 3771 |
. . 3
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12 | 10, 11 | syl6eq 2512 |
. 2
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13 | 2, 12 | syl5eq 2508 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-res 4865 |
This theorem is referenced by: qtophaus 28712 |
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