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Mirrors > Home > MPE Home > Th. List > s1eq | Structured version Unicode version |
Description: Equality theorem for a singleton word. (Contributed by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
s1eq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 5792 |
. . . 4
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2 | 1 | opeq2d 4167 |
. . 3
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3 | 2 | sneqd 3990 |
. 2
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4 | df-s1 12343 |
. 2
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5 | df-s1 12343 |
. 2
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6 | 3, 4, 5 | 3eqtr4g 2517 |
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-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
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-rex 2801 df-rab 2804 df-v 3073 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-nul 3739 df-if 3893 df-sn 3979 df-pr 3981 df-op 3985 df-uni 4193 df-br 4394 df-iota 5482 df-fv 5527 df-s1 12343 |
This theorem is referenced by: s1eqd 12403 wrdl1s1 12412 wrdind 12482 wrd2ind 12483 revs1 12516 vrmdval 15646 frgpup3lem 16387 vdegp1ci 23752 signstfveq0 27115 ccats1swrdeqrex 30400 ccats1rev 30401 reuccats1 30402 wwlkn0 30464 |
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