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Mirrors > Home > ILE Home > Th. List > rexim | Unicode version |
Description: Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
rexim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2395 |
. . . 4
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2 | simpl 108 |
. . . . . . 7
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3 | 2 | a1i 9 |
. . . . . 6
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4 | pm3.31 260 |
. . . . . 6
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5 | 3, 4 | jcad 303 |
. . . . 5
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6 | 5 | alimi 1414 |
. . . 4
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7 | 1, 6 | sylbi 120 |
. . 3
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8 | exim 1561 |
. . 3
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9 | 7, 8 | syl 14 |
. 2
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10 | df-rex 2396 |
. 2
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11 | df-rex 2396 |
. 2
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12 | 9, 10, 11 | 3imtr4g 204 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-4 1470 ax-ial 1497 |
This theorem depends on definitions: df-bi 116 df-ral 2395 df-rex 2396 |
This theorem is referenced by: reximia 2501 reximdai 2504 r19.29 2543 reupick2 3328 ss2iun 3794 chfnrn 5485 |
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