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Mirrors > Home > MPE Home > Th. List > prelpwi | Structured version Visualization version Unicode version |
Description: A pair of two sets belongs to the power class of a class containing those two sets. (Contributed by Thierry Arnoux, 10-Mar-2017.) (Proof shortened by AV, 23-Oct-2021.) |
Ref | Expression |
---|---|
prelpwi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prelpw 4914 | . 2 | |
2 | 1 | ibi 256 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 cpw 4158 cpr 4179 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-pw 4160 df-sn 4178 df-pr 4180 |
This theorem is referenced by: inelfi 8324 elss2prb 13269 isdrs2 16939 usgrexmplef 26151 cusgrexilem2 26338 cusgrfilem2 26352 umgr2v2e 26421 vdegp1bi 26433 eupth2lem3lem5 27092 unelsiga 30197 unelldsys 30221 measxun2 30273 saluncl 40537 prelspr 41736 lincvalpr 42207 ldepspr 42262 zlmodzxzldeplem3 42291 zlmodzxzldep 42293 ldepsnlinc 42297 |
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