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Mirrors > Home > ILE Home > Th. List > mulid1d | Unicode version |
Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 |
Ref | Expression |
---|---|
mulid1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 | . 2 | |
2 | mulid1 7731 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 (class class class)co 5742 cc 7586 c1 7589 cmul 7593 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-resscn 7680 ax-1cn 7681 ax-icn 7683 ax-addcl 7684 ax-mulcl 7686 ax-mulcom 7689 ax-mulass 7691 ax-distr 7692 ax-1rid 7695 ax-cnre 7699 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: muladd11 7863 ltmul1 8322 mulap0 8383 divrecap 8416 diveqap1 8433 conjmulap 8457 apmul1 8516 qapne 9399 divelunit 9753 modqid 10090 q2submod 10126 addmodlteq 10139 expadd 10303 leexp2r 10315 nnlesq 10364 sqoddm1div8 10412 nn0opthlem1d 10434 faclbnd 10455 faclbnd2 10456 faclbnd6 10458 facavg 10460 bcn0 10469 bcn1 10472 reccn2ap 11050 hash2iun1dif1 11217 binom11 11223 trireciplem 11237 geosergap 11243 cvgratnnlemnexp 11261 cvgratnnlemmn 11262 efzval 11316 tanaddaplem 11372 tanaddap 11373 cos01gt0 11396 absef 11403 1dvds 11434 bezoutlema 11614 bezoutlemb 11615 gcdmultiple 11635 sqgcd 11644 lcm1 11689 coprmdvds 11700 qredeu 11705 phiprmpw 11825 dveflem 12782 efper 12815 tangtx 12846 trilpolemclim 13156 trilpolemisumle 13158 trilpolemeq1 13160 trilpolemlt1 13161 |
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