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Mirrors > Home > MPE Home > Th. List > psssstr | Structured version Visualization version Unicode version |
Description: Transitive law for subclass and proper subclass. (Contributed by NM, 3-Apr-1996.) |
Ref | Expression |
---|---|
psssstr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspss 3543 |
. 2
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2 | psstr 3548 |
. . . . 5
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3 | 2 | ex 440 |
. . . 4
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4 | psseq2 3532 |
. . . . 5
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5 | 4 | biimpcd 232 |
. . . 4
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6 | 3, 5 | jaod 386 |
. . 3
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7 | 6 | imp 435 |
. 2
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8 | 1, 7 | sylan2b 482 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-ne 2634 df-in 3422 df-ss 3429 df-pss 3431 |
This theorem is referenced by: psssstrd 3553 suplem1pr 9502 atexch 28082 bj-2upln0 31661 bj-2upln1upl 31662 |
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