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Mirrors > Home > ILE Home > Th. List > sb6x | Unicode version |
Description: Equivalence involving substitution for a variable not free. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) |
Ref | Expression |
---|---|
sb6x.1 |
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Ref | Expression |
---|---|
sb6x |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb6x.1 |
. . 3
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2 | 1 | sbh 1776 |
. 2
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3 | biidd 172 |
. . 3
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4 | 1, 3 | equsalh 1726 |
. 2
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5 | 2, 4 | bitr4i 187 |
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 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-sb 1763 |
This theorem is referenced by: (None) |
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