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Mirrors > Home > NFE Home > Th. List > sbex | Unicode version |
Description: Move existential quantifier in and out of substitution. (Contributed by NM, 27-Sep-2003.) |
Ref | Expression |
---|---|
sbex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbn 2062 |
. . 3
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2 | sbal 2127 |
. . . 4
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3 | sbn 2062 |
. . . . 5
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4 | 3 | albii 1566 |
. . . 4
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5 | 2, 4 | bitri 240 |
. . 3
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6 | 1, 5 | xchbinx 301 |
. 2
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7 | df-ex 1542 |
. . 3
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8 | 7 | sbbii 1653 |
. 2
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9 | df-ex 1542 |
. 2
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10 | 6, 8, 9 | 3bitr4i 268 |
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 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 |
This theorem is referenced by: sbmo 2234 sbabel 2516 sbcex2 3096 sbcexg 3097 |
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