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Mirrors > Home > NFE Home > Th. List > psstr | Unicode version |
Description: Transitive law for proper subclass. Theorem 9 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.) |
Ref | Expression |
---|---|
psstr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pssss 3364 | . . 3 | |
2 | pssss 3364 | . . 3 | |
3 | 1, 2 | sylan9ss 3285 | . 2 |
4 | pssn2lp 3370 | . . . 4 | |
5 | psseq1 3356 | . . . . 5 | |
6 | 5 | anbi1d 685 | . . . 4 |
7 | 4, 6 | mtbiri 294 | . . 3 |
8 | 7 | con2i 112 | . 2 |
9 | dfpss2 3354 | . 2 | |
10 | 3, 8, 9 | sylanbrc 645 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 358 wceq 1642 wss 3257 wpss 3258 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-pss 3261 |
This theorem is referenced by: sspsstr 3374 psssstr 3375 psstrd 3376 |
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