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Mirrors > Home > MPE Home > Th. List > sspss | Structured version Visualization version Unicode version |
Description: Subclass in terms of proper subclass. (Contributed by NM, 25-Feb-1996.) |
Ref | Expression |
---|---|
sspss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfpss2 3692 | . . . . 5 | |
2 | 1 | simplbi2 655 | . . . 4 |
3 | 2 | con1d 139 | . . 3 |
4 | 3 | orrd 393 | . 2 |
5 | pssss 3702 | . . 3 | |
6 | eqimss 3657 | . . 3 | |
7 | 5, 6 | jaoi 394 | . 2 |
8 | 4, 7 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wo 383 wceq 1483 wss 3574 wpss 3575 |
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-ne 2795 df-in 3581 df-ss 3588 df-pss 3590 |
This theorem is referenced by: sspsstri 3709 sspsstr 3712 psssstr 3713 ordsseleq 5752 sorpssuni 6946 sorpssint 6947 ssnnfi 8179 ackbij1b 9061 fin23lem40 9173 zorng 9326 psslinpr 9853 suplem2pr 9875 ressval3d 15937 mrissmrcd 16300 pgpssslw 18029 pgpfac1lem5 18478 idnghm 22547 dfon2lem4 31691 finminlem 32312 lkrss2N 34456 dvh3dim3N 36738 |
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