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Mirrors > Home > MPE Home > Th. List > raltpg | Structured version Visualization version Unicode version |
Description: Convert a quantification over a triple 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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raltpg.3 |
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Ref | Expression |
---|---|
raltpg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralprg.1 |
. . . . 5
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2 | ralprg.2 |
. . . . 5
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3 | 1, 2 | ralprg 4023 |
. . . 4
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4 | raltpg.3 |
. . . . 5
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5 | 4 | ralsng 4008 |
. . . 4
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6 | 3, 5 | bi2anan9 885 |
. . 3
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7 | 6 | 3impa 1204 |
. 2
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8 | df-tp 3975 |
. . . 4
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9 | 8 | raleqi 2993 |
. . 3
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10 | ralunb 3617 |
. . 3
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11 | 9, 10 | bitri 253 |
. 2
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12 | df-3an 988 |
. 2
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13 | 7, 11, 12 | 3bitr4g 292 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ral 2744 df-v 3049 df-sbc 3270 df-un 3411 df-sn 3971 df-pr 3973 df-tp 3975 |
This theorem is referenced by: raltp 4029 raltpd 4098 f13dfv 6178 sumtp 13822 lcmftp 14621 nb3grapr 25193 cusgra3v 25204 3v3e3cycl1 25384 constr3trllem2 25391 constr3trllem5 25394 frgra3v 25742 nb3grpr 39466 |
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