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Mirrors > Home > ILE Home > Th. List > rexprg | Unicode version |
Description: Convert a quantification over a pair to a disjunction. (Contributed by NM, 17-Sep-2011.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralprg.1 |
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ralprg.2 |
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Ref | Expression |
---|---|
rexprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3625 |
. . . 4
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2 | 1 | rexeqi 2695 |
. . 3
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3 | rexun 3339 |
. . 3
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4 | 2, 3 | bitri 184 |
. 2
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5 | ralprg.1 |
. . . . 5
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6 | 5 | rexsng 3659 |
. . . 4
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7 | 6 | orbi1d 792 |
. . 3
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8 | ralprg.2 |
. . . . 5
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9 | 8 | rexsng 3659 |
. . . 4
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10 | 9 | orbi2d 791 |
. . 3
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11 | 7, 10 | sylan9bb 462 |
. 2
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12 | 4, 11 | bitrid 192 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-rex 2478 df-v 2762 df-sbc 2986 df-un 3157 df-sn 3624 df-pr 3625 |
This theorem is referenced by: rextpg 3672 rexpr 3674 minmax 11373 xrminmax 11408 |
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