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Mirrors > Home > ILE Home > Th. List > 1t1e1 | GIF version |
Description: 1 times 1 equals 1. (Contributed by David A. Wheeler, 7-Jul-2016.) |
Ref | Expression |
---|---|
1t1e1 | ⊢ (1 · 1) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 7499 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | mulid1i 7551 | 1 ⊢ (1 · 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1290 (class class class)co 5666 1c1 7412 · cmul 7416 |
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: neg1mulneg1e1 8689 addltmul 8713 1exp 10045 expge1 10053 mulexp 10055 mulexpzap 10056 expaddzap 10060 m1expeven 10063 i4 10118 facp1 10199 binom 10939 rpmul 11419 |
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