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Mirrors > Home > ILE Home > Th. List > ralcom3 | Unicode version |
Description: A commutative law for restricted quantifiers that swaps the domain of the restriction. (Contributed by NM, 22-Feb-2004.) |
Ref | Expression |
---|---|
ralcom3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.04 82 |
. . 3
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2 | 1 | ralimi2 2537 |
. 2
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3 | pm2.04 82 |
. . 3
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4 | 3 | ralimi2 2537 |
. 2
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5 | 2, 4 | impbii 126 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 |
This theorem depends on definitions: df-bi 117 df-ral 2460 |
This theorem is referenced by: zfregfr 4573 tgss2 13510 |
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