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Mirrors > Home > ILE Home > Th. List > ax1rid | Unicode version |
Description: ![]() |
Ref | Expression |
---|---|
ax1rid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-r 7838 |
. 2
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2 | oveq1 5897 |
. . 3
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3 | id 19 |
. . 3
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4 | 2, 3 | eqeq12d 2203 |
. 2
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5 | elsni 3624 |
. . 3
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6 | df-1 7836 |
. . . . . . 7
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7 | 6 | oveq2i 5901 |
. . . . . 6
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8 | 1sr 7767 |
. . . . . . . 8
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9 | mulresr 7854 |
. . . . . . . 8
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10 | 8, 9 | mpan2 425 |
. . . . . . 7
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11 | 1idsr 7784 |
. . . . . . . 8
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12 | 11 | opeq1d 3798 |
. . . . . . 7
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13 | 10, 12 | eqtrd 2221 |
. . . . . 6
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14 | 7, 13 | eqtrid 2233 |
. . . . 5
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15 | opeq2 3793 |
. . . . . . 7
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16 | 15 | oveq1d 5905 |
. . . . . 6
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17 | 16, 15 | eqeq12d 2203 |
. . . . 5
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18 | 14, 17 | imbitrrid 156 |
. . . 4
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19 | 18 | impcom 125 |
. . 3
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20 | 5, 19 | sylan2 286 |
. 2
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21 | 1, 4, 20 | optocl 4716 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2161 ax-14 2162 ax-ext 2170 ax-coll 4132 ax-sep 4135 ax-nul 4143 ax-pow 4188 ax-pr 4223 ax-un 4447 ax-setind 4550 ax-iinf 4601 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-3or 980 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2040 df-mo 2041 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-ne 2360 df-ral 2472 df-rex 2473 df-reu 2474 df-rab 2476 df-v 2753 df-sbc 2977 df-csb 3072 df-dif 3145 df-un 3147 df-in 3149 df-ss 3156 df-nul 3437 df-pw 3591 df-sn 3612 df-pr 3613 df-op 3615 df-uni 3824 df-int 3859 df-iun 3902 df-br 4018 df-opab 4079 df-mpt 4080 df-tr 4116 df-eprel 4303 df-id 4307 df-po 4310 df-iso 4311 df-iord 4380 df-on 4382 df-suc 4385 df-iom 4604 df-xp 4646 df-rel 4647 df-cnv 4648 df-co 4649 df-dm 4650 df-rn 4651 df-res 4652 df-ima 4653 df-iota 5192 df-fun 5232 df-fn 5233 df-f 5234 df-f1 5235 df-fo 5236 df-f1o 5237 df-fv 5238 df-ov 5893 df-oprab 5894 df-mpo 5895 df-1st 6158 df-2nd 6159 df-recs 6323 df-irdg 6388 df-1o 6434 df-2o 6435 df-oadd 6438 df-omul 6439 df-er 6552 df-ec 6554 df-qs 6558 df-ni 7320 df-pli 7321 df-mi 7322 df-lti 7323 df-plpq 7360 df-mpq 7361 df-enq 7363 df-nqqs 7364 df-plqqs 7365 df-mqqs 7366 df-1nqqs 7367 df-rq 7368 df-ltnqqs 7369 df-enq0 7440 df-nq0 7441 df-0nq0 7442 df-plq0 7443 df-mq0 7444 df-inp 7482 df-i1p 7483 df-iplp 7484 df-imp 7485 df-enr 7742 df-nr 7743 df-plr 7744 df-mr 7745 df-0r 7747 df-1r 7748 df-m1r 7749 df-c 7834 df-1 7836 df-r 7838 df-mul 7840 |
This theorem is referenced by: rereceu 7905 recriota 7906 |
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