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Mirrors > Home > ILE Home > Th. List > sbh | Unicode version |
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 17-Oct-2004.) |
Ref | Expression |
---|---|
sbh.1 |
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Ref | Expression |
---|---|
sbh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb1 1740 |
. . . 4
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2 | sbh.1 |
. . . . 5
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3 | 2 | 19.41h 1664 |
. . . 4
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4 | 1, 3 | sylib 121 |
. . 3
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5 | 4 | simprd 113 |
. 2
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6 | stdpc4 1749 |
. . 3
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7 | 2, 6 | syl 14 |
. 2
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8 | 5, 7 | impbii 125 |
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-sb 1737 |
This theorem is referenced by: sbf 1751 sb6x 1753 nfs1f 1754 hbs1f 1755 sbid2h 1822 sblimv 1867 sbrim 1930 sbrbif 1936 elsb3 1952 elsb4 1953 |
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