|   | Mathbox for Steven Nguyen | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > Mathboxes > it1ei | Structured version Visualization version GIF version | ||
| Description: i times 1 equals i. (Contributed by SN, 25-Apr-2025.) | 
| Ref | Expression | 
|---|---|
| it1ei | ⊢ (i · 1) = i | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ax-icn 11215 | . 2 ⊢ i ∈ ℂ | |
| 2 | 1 | mulridi 11266 | 1 ⊢ (i · 1) = i | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1539 (class class class)co 7432 1c1 11157 ici 11158 · cmul 11161 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-resscn 11213 ax-1cn 11214 ax-icn 11215 ax-addcl 11216 ax-mulcl 11218 ax-mulcom 11220 ax-mulass 11222 ax-distr 11223 ax-1rid 11226 ax-cnre 11229 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-rex 3070 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-iota 6513 df-fv 6568 df-ov 7435 | 
| This theorem is referenced by: (None) | 
| Copyright terms: Public domain | W3C validator |