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Mirrors > Home > MPE Home > Th. List > bascnvimaeqv | Structured version Visualization version GIF version |
Description: The inverse image of the universal class V under the base function is the universal class V itself. (Proposed by Mario Carneiro, 7-Mar-2020.) (Contributed by AV, 7-Mar-2020.) |
Ref | Expression |
---|---|
bascnvimaeqv | ⊢ (◡Base “ V) = V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 15910 | . . 3 ⊢ Base = Slot 1 | |
2 | 1 | slotfn 15922 | . 2 ⊢ Base Fn V |
3 | fncnvimaeqv 16807 | . 2 ⊢ (Base Fn V → (◡Base “ V) = V) | |
4 | 2, 3 | ax-mp 5 | 1 ⊢ (◡Base “ V) = V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1523 Vcvv 3231 ◡ccnv 5142 “ cima 5146 Fn wfn 5921 1c1 9975 Basecbs 15904 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-sep 4814 ax-nul 4822 ax-pr 4936 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-eu 2502 df-mo 2503 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ne 2824 df-ral 2946 df-rex 2947 df-rab 2950 df-v 3233 df-sbc 3469 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-nul 3949 df-if 4120 df-sn 4211 df-pr 4213 df-op 4217 df-uni 4469 df-br 4686 df-opab 4746 df-mpt 4763 df-id 5053 df-xp 5149 df-rel 5150 df-cnv 5151 df-co 5152 df-dm 5153 df-rn 5154 df-res 5155 df-ima 5156 df-iota 5889 df-fun 5928 df-fn 5929 df-fv 5934 df-slot 15908 df-base 15910 |
This theorem is referenced by: (None) |
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