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Mirrors > Home > MPE Home > Th. List > wunpw | Structured version Visualization version Unicode version |
Description: A weak universe is closed under powerset. (Contributed by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
wununi.1 | WUni |
wununi.2 |
Ref | Expression |
---|---|
wunpw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wununi.2 | . 2 | |
2 | wununi.1 | . . 3 WUni | |
3 | iswun 9526 | . . . . 5 WUni WUni | |
4 | 3 | ibi 256 | . . . 4 WUni |
5 | 4 | simp3d 1075 | . . 3 WUni |
6 | simp2 1062 | . . . 4 | |
7 | 6 | ralimi 2952 | . . 3 |
8 | 2, 5, 7 | 3syl 18 | . 2 |
9 | pweq 4161 | . . . 4 | |
10 | 9 | eleq1d 2686 | . . 3 |
11 | 10 | rspcv 3305 | . 2 |
12 | 1, 8, 11 | sylc 65 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 w3a 1037 wceq 1483 wcel 1990 wne 2794 wral 2912 c0 3915 cpw 4158 cpr 4179 cuni 4436 wtr 4752 WUnicwun 9522 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-v 3202 df-in 3581 df-ss 3588 df-pw 4160 df-uni 4437 df-tr 4753 df-wun 9524 |
This theorem is referenced by: wunss 9534 wunr1om 9541 wunxp 9546 wunpm 9547 intwun 9557 r1wunlim 9559 wuncval2 9569 wuncn 9991 wunfunc 16559 wunnat 16616 catcoppccl 16758 catcfuccl 16759 catcxpccl 16847 |
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