![]() |
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 7929 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | mulid1i 7984 | 1 ⊢ (1 · 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 (class class class)co 5892 1c1 7837 · cmul 7841 |
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 7928 ax-1cn 7929 ax-icn 7931 ax-addcl 7932 ax-mulcl 7934 ax-mulcom 7937 ax-mulass 7939 ax-distr 7940 ax-1rid 7943 ax-cnre 7947 |
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 5193 df-fv 5240 df-ov 5895 |
This theorem is referenced by: neg1mulneg1e1 9156 addltmul 9180 1exp 10575 expge1 10583 mulexp 10585 mulexpzap 10586 expaddzap 10590 m1expeven 10593 i4 10649 facp1 10737 binom 11519 prodf1 11577 prodfrecap 11581 fprodmul 11626 fprodrec 11664 fprodge1 11674 rpmul 12125 dvexp 14612 dvef 14625 lgslem3 14840 lgsval2lem 14848 lgsneg 14862 lgsdilem 14865 lgsdir 14873 lgsdi 14875 |
Copyright terms: Public domain | W3C validator |