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Mirrors > Home > ILE Home > Th. List > sbft | Unicode version |
Description: Substitution has no effect on a non-free variable. (Contributed by NM, 30-May-2009.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 3-May-2018.) |
Ref | Expression |
---|---|
sbft |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spsbe 1815 |
. . 3
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2 | 19.9t 1622 |
. . 3
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3 | 1, 2 | syl5ib 153 |
. 2
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4 | nfr 1499 |
. . 3
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5 | stdpc4 1749 |
. . 3
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6 | 4, 5 | syl6 33 |
. 2
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7 | 3, 6 | impbid 128 |
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-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: sbctt 2979 |
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