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Mirrors > Home > MPE Home > Th. List > rexab2 | Structured version Unicode version |
Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
ralab2.1 |
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Ref | Expression |
---|---|
rexab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2799 |
. 2
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2 | nfsab1 2440 |
. . . 4
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3 | nfv 1674 |
. . . 4
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4 | 2, 3 | nfan 1863 |
. . 3
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5 | nfv 1674 |
. . 3
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6 | eleq1 2521 |
. . . . 5
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7 | abid 2438 |
. . . . 5
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8 | 6, 7 | syl6bb 261 |
. . . 4
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9 | ralab2.1 |
. . . 4
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10 | 8, 9 | anbi12d 710 |
. . 3
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11 | 4, 5, 10 | cbvex 1979 |
. 2
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12 | 1, 11 | bitri 249 |
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 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-an 371 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-rex 2799 |
This theorem is referenced by: rexrab2 3221 tmdgsum2 19780 |
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