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Mirrors > Home > ILE Home > Th. List > ra5 | Unicode version |
Description: Restricted quantifier version of Axiom 5 of [Mendelson] p. 69. This is an axiom of a predicate calculus for a restricted domain. Compare the unrestricted stdpc5 1564. (Contributed by NM, 16-Jan-2004.) |
Ref | Expression |
---|---|
ra5.1 |
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Ref | Expression |
---|---|
ra5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2422 |
. . . 4
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2 | bi2.04 247 |
. . . . 5
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3 | 2 | albii 1447 |
. . . 4
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4 | 1, 3 | bitri 183 |
. . 3
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5 | ra5.1 |
. . . 4
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6 | 5 | stdpc5 1564 |
. . 3
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7 | 4, 6 | sylbi 120 |
. 2
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8 | df-ral 2422 |
. 2
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9 | 7, 8 | syl6ibr 161 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-4 1488 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-ral 2422 |
This theorem is referenced by: (None) |
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