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Mirrors > Home > ILE Home > Th. List > exan | Unicode version |
Description: Place a conjunct in the scope of an existential quantifier. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
exan.1 |
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Ref | Expression |
---|---|
exan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbe1 1472 |
. . . 4
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2 | 1 | 19.28h 1542 |
. . 3
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3 | exan.1 |
. . 3
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4 | 2, 3 | mpgbi 1429 |
. 2
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5 | 19.29r 1601 |
. 2
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6 | 4, 5 | ax-mp 5 |
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-ie1 1470 ax-ie2 1471 ax-4 1488 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: bm1.3ii 4057 bdbm1.3ii 13260 |
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