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Mirrors > Home > MPE Home > Th. List > axgroth5 | Structured version Unicode version |
Description: The Tarski-Grothendieck axiom using abbreviations. (Contributed by NM, 22-Jun-2009.) |
Ref | Expression |
---|---|
axgroth5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-groth 9096 |
. 2
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2 | biid 236 |
. . . 4
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3 | pwss 3978 |
. . . . . 6
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4 | pwss 3978 |
. . . . . . 7
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5 | 4 | rexbii 2861 |
. . . . . 6
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6 | 3, 5 | anbi12i 697 |
. . . . 5
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7 | 6 | ralbii 2836 |
. . . 4
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8 | df-ral 2801 |
. . . . 5
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9 | selpw 3970 |
. . . . . . 7
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10 | 9 | imbi1i 325 |
. . . . . 6
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11 | 10 | albii 1611 |
. . . . 5
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12 | 8, 11 | bitri 249 |
. . . 4
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13 | 2, 7, 12 | 3anbi123i 1177 |
. . 3
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14 | 13 | exbii 1635 |
. 2
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15 | 1, 14 | mpbir 209 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 ax-groth 9096 |
This theorem depends on definitions: df-bi 185 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ral 2801 df-rex 2802 df-v 3074 df-in 3438 df-ss 3445 df-pw 3965 |
This theorem is referenced by: grothpw 9099 grothpwex 9100 axgroth6 9101 grothtsk 9108 |
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