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Mirrors > Home > NFE Home > Th. List > ralprg | Unicode version |
Description: Convert a quantification over a pair to a conjunction. (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 |
---|---|
ralprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3743 |
. . . 4
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2 | 1 | raleqi 2812 |
. . 3
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3 | ralunb 3445 |
. . 3
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4 | 2, 3 | bitri 240 |
. 2
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5 | ralprg.1 |
. . . 4
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6 | 5 | ralsng 3766 |
. . 3
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7 | ralprg.2 |
. . . 4
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8 | 7 | ralsng 3766 |
. . 3
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9 | 6, 8 | bi2anan9 843 |
. 2
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10 | 4, 9 | syl5bb 248 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ral 2620 df-v 2862 df-sbc 3048 df-nin 3212 df-compl 3213 df-un 3215 df-sn 3742 df-pr 3743 |
This theorem is referenced by: raltpg 3778 ralpr 3780 iinxprg 4044 |
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