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Mirrors > Home > NFE Home > Th. List > cbvrexdva2 | Unicode version |
Description: Rule used to change the bound variable in a restricted existential quantifier with implicit substitution which also changes the quantifier domain. Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
cbvraldva2.1 |
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cbvraldva2.2 |
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Ref | Expression |
---|---|
cbvrexdva2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 447 |
. . . . 5
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2 | cbvraldva2.2 |
. . . . 5
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3 | 1, 2 | eleq12d 2421 |
. . . 4
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4 | cbvraldva2.1 |
. . . 4
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5 | 3, 4 | anbi12d 691 |
. . 3
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6 | 5 | cbvexdva 2011 |
. 2
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7 | df-rex 2621 |
. 2
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8 | df-rex 2621 |
. 2
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9 | 6, 7, 8 | 3bitr4g 279 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-cleq 2346 df-clel 2349 df-rex 2621 |
This theorem is referenced by: cbvrexdva 2843 |
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