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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 7681 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | mulid1i 7736 | 1 ⊢ (1 · 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 (class class class)co 5742 1c1 7589 · cmul 7593 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-resscn 7680 ax-1cn 7681 ax-icn 7683 ax-addcl 7684 ax-mulcl 7686 ax-mulcom 7689 ax-mulass 7691 ax-distr 7692 ax-1rid 7695 ax-cnre 7699 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: neg1mulneg1e1 8900 addltmul 8924 1exp 10290 expge1 10298 mulexp 10300 mulexpzap 10301 expaddzap 10305 m1expeven 10308 i4 10363 facp1 10444 binom 11221 rpmul 11706 dvexp 12771 dvef 12783 |
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