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Mirrors > Home > MPE Home > Th. List > cbvexd | Structured version Unicode version |
Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 2036. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
cbvald.1 |
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cbvald.2 |
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cbvald.3 |
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Ref | Expression |
---|---|
cbvexd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvald.1 |
. . . 4
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2 | cbvald.2 |
. . . . 5
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3 | 2 | nfnd 1838 |
. . . 4
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4 | cbvald.3 |
. . . . 5
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5 | notbi 295 |
. . . . 5
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6 | 4, 5 | syl6ib 226 |
. . . 4
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7 | 1, 3, 6 | cbvald 1982 |
. . 3
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8 | 7 | notbid 294 |
. 2
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9 | df-ex 1588 |
. 2
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10 | df-ex 1588 |
. 2
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11 | 8, 9, 10 | 3bitr4g 288 |
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 1952 |
This theorem depends on definitions: df-bi 185 df-an 371 df-ex 1588 df-nf 1591 |
This theorem is referenced by: cbvexdva 1990 vtoclgft 3118 dfid3 4737 axrepndlem2 8860 axunnd 8863 axpowndlem2 8865 axpowndlem2OLD 8866 axpownd 8870 axregndlem2 8872 axinfndlem1 8875 axacndlem4 8880 wl-mo2dnae 28535 wl-mo2t 28536 |
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