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Mirrors > Home > MPE Home > Th. List > rspc3v | Structured version Visualization version Unicode version |
Description: 3-variable restricted specialization, using implicit substitution. (Contributed by NM, 10-May-2005.) |
Ref | Expression |
---|---|
rspc3v.1 |
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rspc3v.2 |
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rspc3v.3 |
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Ref | Expression |
---|---|
rspc3v |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspc3v.1 |
. . . . 5
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2 | 1 | ralbidv 2809 |
. . . 4
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3 | rspc3v.2 |
. . . . 5
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4 | 3 | ralbidv 2809 |
. . . 4
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5 | 2, 4 | rspc2v 3126 |
. . 3
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6 | rspc3v.3 |
. . . 4
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7 | 6 | rspcv 3113 |
. . 3
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8 | 5, 7 | sylan9 667 |
. 2
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9 | 8 | 3impa 1205 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 190 df-an 377 df-3an 988 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ral 2741 df-v 3014 |
This theorem is referenced by: swopolem 4741 isopolem 6221 caovassg 6454 caovcang 6457 caovordig 6461 caovordg 6463 caovdig 6470 caovdirg 6473 caofass 6552 caoftrn 6553 prslem 16186 posi 16205 latdisdlem 16445 dlatmjdi 16450 sgrpass 16543 gaass 16961 islmodd 18107 lsscl 18176 assalem 18550 psmettri2 21335 xmettri2 21365 axtgcgrid 24522 axtg5seg 24524 axtgpasch 24526 axtgupdim2 24530 axtgeucl 24531 tgdim01 24562 f1otrgitv 24911 grpoass 25942 isgrp2d 25974 rngodi 26124 rngodir 26125 rngoass 26126 vcdi 26182 vcdir 26183 vcass 26184 lnolin 26406 lnopl 27578 lnfnl 27595 omndadd 28475 axtgupdim2OLD 29490 lfli 32628 cvlexch1 32895 rngdir 40206 |
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