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Mirrors > Home > MPE Home > Th. List > ralf0 | Structured version Visualization version Unicode version |
Description: The quantification of a falsehood is vacuous when true. (Contributed by NM, 26-Nov-2005.) |
Ref | Expression |
---|---|
ralf0.1 |
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Ref | Expression |
---|---|
ralf0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralf0.1 |
. . . . 5
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2 | con3 140 |
. . . . 5
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3 | 1, 2 | mpi 20 |
. . . 4
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4 | 3 | alimi 1686 |
. . 3
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5 | df-ral 2744 |
. . 3
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6 | eq0 3749 |
. . 3
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7 | 4, 5, 6 | 3imtr4i 270 |
. 2
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8 | rzal 3873 |
. 2
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9 | 7, 8 | impbii 191 |
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-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-v 3049 df-dif 3409 df-nul 3734 |
This theorem is referenced by: uvtx01vtx 25232 rusgra0edg 25695 |
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