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Mirrors > Home > MPE Home > Th. List > gencbvex | Structured version Visualization version Unicode version |
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
gencbvex.1 |
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gencbvex.2 |
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gencbvex.3 |
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gencbvex.4 |
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Ref | Expression |
---|---|
gencbvex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1930 |
. 2
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2 | gencbvex.1 |
. . . 4
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3 | gencbvex.3 |
. . . . . . 7
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4 | gencbvex.2 |
. . . . . . 7
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5 | 3, 4 | anbi12d 722 |
. . . . . 6
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6 | 5 | bicomd 206 |
. . . . 5
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7 | 6 | eqcoms 2459 |
. . . 4
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8 | 2, 7 | ceqsexv 3051 |
. . 3
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9 | 8 | exbii 1721 |
. 2
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10 | 19.41v 1833 |
. . . 4
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11 | simpr 467 |
. . . . 5
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12 | gencbvex.4 |
. . . . . . . 8
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13 | eqcom 2458 |
. . . . . . . . . . 11
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14 | 13 | biimpi 199 |
. . . . . . . . . 10
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15 | 14 | adantl 472 |
. . . . . . . . 9
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16 | 15 | eximi 1710 |
. . . . . . . 8
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17 | 12, 16 | sylbi 200 |
. . . . . . 7
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18 | 17 | adantr 471 |
. . . . . 6
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19 | 18 | ancri 559 |
. . . . 5
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20 | 11, 19 | impbii 192 |
. . . 4
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21 | 10, 20 | bitri 257 |
. . 3
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22 | 21 | exbii 1721 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 9, 22 | 3bitr3i 283 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-10 1918 ax-11 1923 ax-12 1936 ax-ext 2431 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-clab 2438 df-cleq 2444 df-clel 2447 df-v 3014 |
This theorem is referenced by: gencbvex2 3060 gencbval 3061 |
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