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Mirrors > Home > ILE Home > Th. List > mulid2d | Unicode version |
Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 |
Ref | Expression |
---|---|
mulid2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 | . 2 | |
2 | mulid2 7025 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 (class class class)co 5512 cc 6887 c1 6890 cmul 6894 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-resscn 6976 ax-1cn 6977 ax-icn 6979 ax-addcl 6980 ax-mulcl 6982 ax-mulcom 6985 ax-mulass 6987 ax-distr 6988 ax-1rid 6991 ax-cnre 6995 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 |
This theorem is referenced by: mulsubfacd 7415 mulcanapd 7642 receuap 7650 divdivdivap 7689 divcanap5 7690 ltrec 7849 recp1lt1 7865 nndivtr 7955 gtndiv 8335 lincmb01cmp 8871 iccf1o 8872 modqfrac 9179 m1expcl2 9277 expgt1 9293 ltexp2a 9306 leexp2a 9307 binom3 9366 cvg1nlemcau 9583 resqrexlemover 9608 resqrexlemcalc2 9613 absimle 9680 qdencn 10124 |
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