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Mirrors > Home > ILE Home > Th. List > sbex | Unicode version |
Description: Move existential quantifier in and out of substitution. (Contributed by NM, 27-Sep-2003.) (Proof rewritten by Jim Kingdon, 12-Feb-2018.) |
Ref | Expression |
---|---|
sbex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbexyz 2015 |
. . . 4
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2 | 1 | sbbii 1776 |
. . 3
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3 | sbexyz 2015 |
. . 3
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4 | 2, 3 | bitri 184 |
. 2
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5 | ax-17 1537 |
. . 3
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6 | 5 | sbco2vh 1957 |
. 2
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7 | ax-17 1537 |
. . . 4
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8 | 7 | sbco2vh 1957 |
. . 3
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9 | 8 | exbii 1616 |
. 2
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10 | 4, 6, 9 | 3bitr3i 210 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: sbabel 2359 sbcex2 3031 sbcexg 3032 |
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