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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 | mulrid 7984 |
. 2
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3 | 1, 2 | ax-mp 5 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-resscn 7933 ax-1cn 7934 ax-icn 7936 ax-addcl 7937 ax-mulcl 7939 ax-mulcom 7942 ax-mulass 7944 ax-distr 7945 ax-1rid 7948 ax-cnre 7952 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5899 |
This theorem is referenced by: rimul 8572 muleqadd 8655 1t1e1 9101 2t1e2 9102 3t1e3 9104 halfpm6th 9169 iap0 9172 9p1e10 9416 numltc 9439 numsucc 9453 dec10p 9456 numadd 9460 numaddc 9461 11multnc 9481 4t3lem 9510 5t2e10 9513 9t11e99 9543 rei 10940 imi 10941 cji 10943 0.999... 11561 efival 11772 ef01bndlem 11796 3lcm2e6 12192 dveflem 14647 efhalfpi 14680 |
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