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Mirrors > Home > MPE Home > Th. List > trsucss | Structured version Visualization version Unicode version |
Description: A member of the successor of a transitive class is a subclass of it. (Contributed by NM, 4-Oct-2003.) |
Ref | Expression |
---|---|
trsucss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elsuci 5489 |
. 2
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2 | trss 4506 |
. . 3
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3 | eqimss 3484 |
. . . 4
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4 | 3 | a1i 11 |
. . 3
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5 | 2, 4 | jaod 382 |
. 2
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6 | 1, 5 | syl5 33 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ral 2742 df-v 3047 df-un 3409 df-in 3411 df-ss 3418 df-sn 3969 df-uni 4199 df-tr 4498 df-suc 5429 |
This theorem is referenced by: efgmnvl 17364 |
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