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Mirrors > Home > MPE Home > Th. List > sess2 | Structured version Visualization version Unicode version |
Description: Subset theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
sess2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssralv 3495 |
. . 3
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2 | rabss2 3514 |
. . . . 5
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3 | ssexg 4552 |
. . . . . 6
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4 | 3 | ex 436 |
. . . . 5
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5 | 2, 4 | syl 17 |
. . . 4
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6 | 5 | ralimdv 2800 |
. . 3
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7 | 1, 6 | syld 45 |
. 2
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8 | df-se 4797 |
. 2
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9 | df-se 4797 |
. 2
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10 | 7, 8, 9 | 3imtr4g 274 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ral 2744 df-rab 2748 df-v 3049 df-in 3413 df-ss 3420 df-se 4797 |
This theorem is referenced by: seeq2 4810 wereu2 4834 wfrlem5 7045 frmin 30492 frrlem5 30530 |
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