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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 |
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Ref | Expression |
---|---|
mulid1d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 |
. 2
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2 | mulid1 7388 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-resscn 7340 ax-1cn 7341 ax-icn 7343 ax-addcl 7344 ax-mulcl 7346 ax-mulcom 7349 ax-mulass 7351 ax-distr 7352 ax-1rid 7355 ax-cnre 7359 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2614 df-un 2988 df-in 2990 df-ss 2997 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-br 3812 df-iota 4934 df-fv 4977 df-ov 5594 |
This theorem is referenced by: muladd11 7518 ltmul1 7969 mulap0 8021 divrecap 8053 diveqap1 8070 conjmulap 8094 apmul1 8153 qapne 9019 divelunit 9314 modqid 9645 q2submod 9681 addmodlteq 9694 expadd 9834 leexp2r 9846 nnlesq 9894 sqoddm1div8 9941 nn0opthlem1d 9963 faclbnd 9984 faclbnd2 9985 faclbnd6 9987 facavg 9989 bcn0 9998 bcn1 10001 1dvds 10590 bezoutlema 10768 bezoutlemb 10769 gcdmultiple 10789 sqgcd 10798 lcm1 10843 coprmdvds 10854 qredeu 10859 phiprmpw 10978 |
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