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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 11790 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | mulid1i 10716 | 1 ⊢ (3 · 1) = 3 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 (class class class)co 7164 1c1 10609 · cmul 10613 3c3 11765 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1916 ax-6 1974 ax-7 2019 ax-8 2115 ax-9 2123 ax-ext 2710 ax-resscn 10665 ax-1cn 10666 ax-icn 10667 ax-addcl 10668 ax-mulcl 10670 ax-mulcom 10672 ax-mulass 10674 ax-distr 10675 ax-1rid 10678 ax-cnre 10681 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3an 1090 df-tru 1545 df-ex 1787 df-sb 2074 df-clab 2717 df-cleq 2730 df-clel 2811 df-ral 3058 df-rex 3059 df-v 3399 df-un 3846 df-in 3848 df-ss 3858 df-sn 4514 df-pr 4516 df-op 4520 df-uni 4794 df-br 5028 df-iota 6291 df-fv 6341 df-ov 7167 df-2 11772 df-3 11773 |
This theorem is referenced by: 3t3e9 11876 sqrlem7 14691 5prm 16538 631prm 16556 4001prm 16574 pigt3 25254 lhe4.4ex1a 41469 stoweidlem13 43080 3ndvds4 44565 |
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