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Mirrors > Home > MPE Home > Th. List > 3sstr3g | 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 |
---|---|
3sstr3g.1 | |
3sstr3g.2 | |
3sstr3g.3 |
Ref | Expression |
---|---|
3sstr3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr3g.1 | . 2 | |
2 | 3sstr3g.2 | . . 3 | |
3 | 3sstr3g.3 | . . 3 | |
4 | 2, 3 | sseq12i 3631 | . 2 |
5 | 1, 4 | sylib 208 | 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: complss 3751 uniintsn 4514 fpwwe2lem13 9464 hmeocls 21571 hmeontr 21572 usgrumgruspgr 26075 chsscon3i 28320 pjss1coi 29022 mdslmd2i 29189 ssbnd 33587 bnd2lem 33590 trclubgNEW 37925 nzss 38516 |
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