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Mirrors > Home > MPE Home > Th. List > s2eqd | Structured version Visualization version Unicode version |
Description: Equality theorem for a doubleton word. (Contributed by Mario Carneiro, 27-Feb-2016.) |
Ref | Expression |
---|---|
s2eqd.1 |
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s2eqd.2 |
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Ref | Expression |
---|---|
s2eqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | s2eqd.1 |
. . . 4
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2 | 1 | s1eqd 12793 |
. . 3
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3 | s2eqd.2 |
. . . 4
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4 | 3 | s1eqd 12793 |
. . 3
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5 | 2, 4 | oveq12d 6326 |
. 2
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6 | df-s2 13003 |
. 2
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7 | df-s2 13003 |
. 2
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8 | 5, 6, 7 | 3eqtr4g 2530 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-iota 5553 df-fv 5597 df-ov 6311 df-s1 12714 df-s2 13003 |
This theorem is referenced by: s3eqd 13019 wrdl2exs2 13097 swrd2lsw 13102 efgi 17447 efgi0 17448 efgi1 17449 efgtf 17450 efgtval 17451 efgval2 17452 frgpuplem 17500 |
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