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Mirrors > Home > ILE Home > Th. List > mulid1i | Unicode version |
Description: Identity law for multiplication. (Contributed by NM, 14-Feb-1995.) |
Ref | Expression |
---|---|
axi.1 |
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Ref | Expression |
---|---|
mulid1i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.1 |
. 2
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2 | mulid1 7546 |
. 2
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3 | 1, 2 | ax-mp 7 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-resscn 7498 ax-1cn 7499 ax-icn 7501 ax-addcl 7502 ax-mulcl 7504 ax-mulcom 7507 ax-mulass 7509 ax-distr 7510 ax-1rid 7513 ax-cnre 7517 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-iota 4993 df-fv 5036 df-ov 5669 |
This theorem is referenced by: rimul 8123 muleqadd 8198 1t1e1 8629 2t1e2 8630 3t1e3 8632 halfpm6th 8697 iap0 8700 9p1e10 8940 numltc 8963 numsucc 8977 dec10p 8980 numadd 8984 numaddc 8985 11multnc 9005 4t3lem 9034 5t2e10 9037 9t11e99 9067 rei 10394 imi 10395 cji 10397 0.999... 10976 efival 11084 ef01bndlem 11108 3lcm2e6 11478 |
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