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Mirrors > Home > ILE Home > Th. List > sbft | Unicode version |
Description: Substitution has no effect on a nonfree 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 1853 |
. . 3
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2 | 19.9t 1653 |
. . 3
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3 | 1, 2 | imbitrid 154 |
. 2
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4 | nfr 1529 |
. . 3
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5 | stdpc4 1786 |
. . 3
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6 | 4, 5 | syl6 33 |
. 2
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7 | 3, 6 | impbid 129 |
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-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: sbctt 3044 |
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