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Mirrors > Home > ILE Home > Th. List > sbequ8 | Unicode version |
Description: Elimination of equality from antecedent after substitution. (Contributed by NM, 5-Aug-1993.) (Proof revised by Jim Kingdon, 20-Jan-2018.) |
Ref | Expression |
---|---|
sbequ8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.4 248 |
. . 3
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2 | simpl 108 |
. . . . . 6
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3 | pm3.35 345 |
. . . . . 6
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4 | 2, 3 | jca 304 |
. . . . 5
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5 | simpl 108 |
. . . . . 6
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6 | pm3.4 331 |
. . . . . 6
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7 | 5, 6 | jca 304 |
. . . . 5
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8 | 4, 7 | impbii 125 |
. . . 4
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9 | 8 | exbii 1585 |
. . 3
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10 | 1, 9 | anbi12i 456 |
. 2
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11 | df-sb 1737 |
. 2
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12 | df-sb 1737 |
. 2
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13 | 10, 11, 12 | 3bitr4ri 212 |
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-ial 1515 |
This theorem depends on definitions: df-bi 116 df-sb 1737 |
This theorem is referenced by: sbidm 1824 |
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