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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 11460 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | mulid1i 10383 | 1 ⊢ (3 · 1) = 3 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1601 (class class class)co 6924 1c1 10275 · cmul 10279 3c3 11435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 ax-ext 2754 ax-resscn 10331 ax-1cn 10332 ax-icn 10333 ax-addcl 10334 ax-mulcl 10336 ax-mulcom 10338 ax-mulass 10340 ax-distr 10341 ax-1rid 10344 ax-cnre 10347 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-3an 1073 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-ral 3095 df-rex 3096 df-rab 3099 df-v 3400 df-dif 3795 df-un 3797 df-in 3799 df-ss 3806 df-nul 4142 df-if 4308 df-sn 4399 df-pr 4401 df-op 4405 df-uni 4674 df-br 4889 df-iota 6101 df-fv 6145 df-ov 6927 df-2 11442 df-3 11443 |
This theorem is referenced by: 3t3e9 11553 sqrlem7 14400 5prm 16218 631prm 16236 4001prm 16254 pigt3 34032 lhe4.4ex1a 39494 stoweidlem13 41167 3ndvds4 42541 |
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