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Mirrors > Home > NFE Home > Th. List > clos1eq2 | Unicode version |
Description: Equality law for closure. (Contributed by SF, 11-Feb-2015.) |
Ref | Expression |
---|---|
clos1eq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imaeq1 4937 |
. . . . . 6
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2 | 1 | sseq1d 3298 |
. . . . 5
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3 | 2 | anbi2d 684 |
. . . 4
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4 | 3 | abbidv 2467 |
. . 3
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5 | inteq 3929 |
. . 3
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6 | 4, 5 | syl 15 |
. 2
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7 | df-clos1 5873 |
. 2
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8 | df-clos1 5873 |
. 2
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9 | 6, 7, 8 | 3eqtr4g 2410 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-int 3927 df-br 4640 df-ima 4727 df-clos1 5873 |
This theorem is referenced by: clos1exg 5877 clos1basesucg 5884 freceq12 6311 |
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