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Mirrors > Home > MPE Home > Th. List > 3t1e3 | Structured version Visualization version GIF version |
Description: 3 times 1 equals 3. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
3t1e3 | ⊢ (3 · 1) = 3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3cn 12315 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | mulridi 11240 | 1 ⊢ (3 · 1) = 3 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 (class class class)co 7414 1c1 11131 · cmul 11135 3c3 12290 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2698 ax-resscn 11187 ax-1cn 11188 ax-icn 11189 ax-addcl 11190 ax-mulcl 11192 ax-mulcom 11194 ax-mulass 11196 ax-distr 11197 ax-1rid 11200 ax-cnre 11203 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-rex 3066 df-rab 3428 df-v 3471 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4319 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-br 5143 df-iota 6494 df-fv 6550 df-ov 7417 df-2 12297 df-3 12298 |
This theorem is referenced by: 3t3e9 12401 01sqrexlem7 15219 5prm 17069 631prm 17087 4001prm 17105 pigt3 26439 lhe4.4ex1a 43689 stoweidlem13 45324 3ndvds4 46858 |
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