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Mirrors > Home > MPE Home > Th. List > ralpr | Structured version Unicode version |
Description: Convert a quantification over a pair to a conjunction. (Contributed by NM, 3-Jun-2007.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralpr.1 |
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ralpr.2 |
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ralpr.3 |
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ralpr.4 |
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Ref | Expression |
---|---|
ralpr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralpr.1 |
. 2
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2 | ralpr.2 |
. 2
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3 | ralpr.3 |
. . 3
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4 | ralpr.4 |
. . 3
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5 | 3, 4 | ralprg 4036 |
. 2
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6 | 1, 2, 5 | mp2an 672 |
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 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ral 2804 df-v 3080 df-sbc 3295 df-un 3444 df-sn 3989 df-pr 3991 |
This theorem is referenced by: fzprval 11638 xpsfrnel 14624 xpsle 14642 isdrs2 15232 pmtrsn 16148 iblcnlem1 21408 wlkntrllem2 23638 wlkntrllem3 23639 2wlklem 23642 subfacp1lem3 27237 fprb 27751 usgra2pthspth 30466 usgra2wlkspthlem1 30467 numclwwlkovf2ex 30850 ldepsnlinc 31205 |
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