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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 12345 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | mulridi 11263 | 1 ⊢ (3 · 1) = 3 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 (class class class)co 7431 1c1 11154 · cmul 11158 3c3 12320 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-resscn 11210 ax-1cn 11211 ax-icn 11212 ax-addcl 11213 ax-mulcl 11215 ax-mulcom 11217 ax-mulass 11219 ax-distr 11220 ax-1rid 11223 ax-cnre 11226 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-rex 3069 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-br 5149 df-iota 6516 df-fv 6571 df-ov 7434 df-2 12327 df-3 12328 |
This theorem is referenced by: 3t3e9 12431 01sqrexlem7 15284 5prm 17143 631prm 17161 4001prm 17179 pigt3 26575 lhe4.4ex1a 44325 stoweidlem13 45969 minusmodnep2tmod 47293 3ndvds4 47520 |
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