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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 7854 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | mulid1i 7909 | 1 ⊢ (1 · 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 (class class class)co 5850 1c1 7762 · cmul 7766 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-resscn 7853 ax-1cn 7854 ax-icn 7856 ax-addcl 7857 ax-mulcl 7859 ax-mulcom 7862 ax-mulass 7864 ax-distr 7865 ax-1rid 7868 ax-cnre 7872 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-iota 5158 df-fv 5204 df-ov 5853 |
This theorem is referenced by: neg1mulneg1e1 9077 addltmul 9101 1exp 10492 expge1 10500 mulexp 10502 mulexpzap 10503 expaddzap 10507 m1expeven 10510 i4 10565 facp1 10651 binom 11434 prodf1 11492 prodfrecap 11496 fprodmul 11541 fprodrec 11579 fprodge1 11589 rpmul 12039 dvexp 13390 dvef 13403 lgslem3 13618 lgsval2lem 13626 lgsneg 13640 lgsdilem 13643 lgsdir 13651 lgsdi 13653 |
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