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Mirrors > Home > MPE Home > Th. List > opelopab | Structured version Visualization version Unicode version |
Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 16-May-1995.) |
Ref | Expression |
---|---|
opelopab.1 |
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opelopab.2 |
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opelopab.3 |
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opelopab.4 |
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Ref | Expression |
---|---|
opelopab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopab.1 |
. 2
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2 | opelopab.2 |
. 2
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3 | opelopab.3 |
. . 3
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4 | opelopab.4 |
. . 3
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5 | 3, 4 | opelopabg 4733 |
. 2
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6 | 1, 2, 5 | mp2an 683 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4476 |
This theorem is referenced by: opabid2 4983 dfres2 5176 f1oiso 6267 elopabi 6881 xporderlem 6934 cnlnssadj 27782 areacirclem5 32081 dicopelval 34790 dih1dimatlem 34942 pellexlem3 35720 |
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