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Mirrors > Home > MPE Home > Th. List > seeq1 | Structured version Visualization version Unicode version |
Description: Equality theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
seeq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3485 |
. . 3
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2 | sess1 4802 |
. . 3
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3 | 1, 2 | syl 17 |
. 2
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4 | eqimss 3484 |
. . 3
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5 | sess1 4802 |
. . 3
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6 | 4, 5 | syl 17 |
. 2
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7 | 3, 6 | impbid 194 |
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 ax-sep 4525 |
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-rab 2746 df-v 3047 df-in 3411 df-ss 3418 df-br 4403 df-se 4794 |
This theorem is referenced by: oieq1 8027 |
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