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Mirrors > Home > MPE Home > Th. List > nqereq | Structured version Unicode version |
Description: The function ![]() |
Ref | Expression |
---|---|
nqereq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nqercl 9198 |
. . . . 5
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2 | 1 | 3ad2ant1 1009 |
. . . 4
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3 | nqercl 9198 |
. . . . 5
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4 | 3 | 3ad2ant2 1010 |
. . . 4
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5 | enqer 9188 |
. . . . . 6
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6 | 5 | a1i 11 |
. . . . 5
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7 | nqerrel 9199 |
. . . . . . 7
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8 | 7 | 3ad2ant1 1009 |
. . . . . 6
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9 | simp3 990 |
. . . . . 6
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10 | 6, 8, 9 | ertr3d 7216 |
. . . . 5
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11 | nqerrel 9199 |
. . . . . 6
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12 | 11 | 3ad2ant2 1010 |
. . . . 5
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13 | 6, 10, 12 | ertrd 7214 |
. . . 4
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14 | enqeq 9201 |
. . . 4
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15 | 2, 4, 13, 14 | syl3anc 1219 |
. . 3
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16 | 15 | 3expia 1190 |
. 2
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17 | 5 | a1i 11 |
. . . 4
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18 | 7 | adantr 465 |
. . . . 5
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19 | simprr 756 |
. . . . 5
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20 | 18, 19 | breqtrd 4411 |
. . . 4
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21 | 11 | ad2antrl 727 |
. . . 4
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22 | 17, 20, 21 | ertr4d 7217 |
. . 3
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23 | 22 | expr 615 |
. 2
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24 | 16, 23 | impbid 191 |
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-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4508 ax-nul 4516 ax-pow 4565 ax-pr 4626 ax-un 6469 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2599 df-ne 2644 df-ral 2798 df-rex 2799 df-reu 2800 df-rmo 2801 df-rab 2802 df-v 3067 df-sbc 3282 df-csb 3384 df-dif 3426 df-un 3428 df-in 3430 df-ss 3437 df-pss 3439 df-nul 3733 df-if 3887 df-pw 3957 df-sn 3973 df-pr 3975 df-tp 3977 df-op 3979 df-uni 4187 df-iun 4268 df-br 4388 df-opab 4446 df-mpt 4447 df-tr 4481 df-eprel 4727 df-id 4731 df-po 4736 df-so 4737 df-fr 4774 df-we 4776 df-ord 4817 df-on 4818 df-lim 4819 df-suc 4820 df-xp 4941 df-rel 4942 df-cnv 4943 df-co 4944 df-dm 4945 df-rn 4946 df-res 4947 df-ima 4948 df-iota 5476 df-fun 5515 df-fn 5516 df-f 5517 df-f1 5518 df-fo 5519 df-f1o 5520 df-fv 5521 df-ov 6190 df-oprab 6191 df-mpt2 6192 df-om 6574 df-1st 6674 df-2nd 6675 df-recs 6929 df-rdg 6963 df-1o 7017 df-oadd 7021 df-omul 7022 df-er 7198 df-ni 9139 df-mi 9141 df-lti 9142 df-enq 9178 df-nq 9179 df-erq 9180 df-1nq 9183 |
This theorem is referenced by: adderpq 9223 mulerpq 9224 distrnq 9228 recmulnq 9231 ltexnq 9242 |
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