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Mirrors > Home > MPE Home > Th. List > decex | Structured version Visualization version GIF version |
Description: A decimal number is a set. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
decex | ⊢ ;𝐴𝐵 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dec 12100 | . 2 ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵) | |
2 | 1 | ovexi 7190 | 1 ⊢ ;𝐴𝐵 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 Vcvv 3494 (class class class)co 7156 1c1 10538 + caddc 10540 · cmul 10542 9c9 11700 ;cdc 12099 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 ax-nul 5210 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-v 3496 df-sbc 3773 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-sn 4568 df-pr 4570 df-uni 4839 df-iota 6314 df-fv 6363 df-ov 7159 df-dec 12100 |
This theorem is referenced by: nfermltl2rev 43928 |
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