Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 7069 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | mulid1i 7121 | 1 ⊢ (1 · 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1284 (class class class)co 5532 1c1 6982 · cmul 6986 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-resscn 7068 ax-1cn 7069 ax-icn 7071 ax-addcl 7072 ax-mulcl 7074 ax-mulcom 7077 ax-mulass 7079 ax-distr 7080 ax-1rid 7083 ax-cnre 7087 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 |
This theorem is referenced by: neg1mulneg1e1 8243 addltmul 8267 1exp 9505 expge1 9513 mulexp 9515 mulexpzap 9516 expaddzap 9520 m1expeven 9523 i4 9577 facp1 9657 rpmul 10480 |
Copyright terms: Public domain | W3C validator |