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Mirrors > Home > MPE Home > Th. List > 3sstr3d | Structured version Visualization version Unicode version |
Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 1-Oct-2000.) |
Ref | Expression |
---|---|
3sstr3d.1 | |
3sstr3d.2 | |
3sstr3d.3 |
Ref | Expression |
---|---|
3sstr3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr3d.1 | . 2 | |
2 | 3sstr3d.2 | . . 3 | |
3 | 3sstr3d.3 | . . 3 | |
4 | 2, 3 | sseq12d 3634 | . 2 |
5 | 1, 4 | mpbid 222 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wss 3574 |
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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-in 3581 df-ss 3588 |
This theorem is referenced by: cnvtsr 17222 dprdss 18428 dprd2da 18441 dmdprdsplit2lem 18444 mplind 19502 txcmplem1 21444 setsmstopn 22283 tngtopn 22454 bcthlem2 23122 bcthlem4 23124 uniiccvol 23348 dyadmaxlem 23365 dvlip2 23758 dvne0 23774 shlej2 28220 hauseqcn 29941 bnd2lem 33590 heiborlem8 33617 dochord 36659 lclkrlem2p 36811 mapdsn 36930 hbtlem5 37698 fvmptiunrelexplb0d 37976 fvmptiunrelexplb1d 37978 |
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