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Mirrors > Home > MPE Home > Th. List > psssstrd | Structured version Visualization version Unicode version |
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 3713. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
psssstrd.1 | |
psssstrd.2 |
Ref | Expression |
---|---|
psssstrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | psssstrd.1 | . 2 | |
2 | psssstrd.2 | . 2 | |
3 | psssstr 3713 | . 2 | |
4 | 1, 2, 3 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 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: ackbij1lem15 9056 lsatssn0 34289 lsatexch 34330 lsatcvatlem 34336 lkrpssN 34450 |
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