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Mirrors > Home > ILE Home > Th. List > sbiedh | Unicode version |
Description: Conversion of implicit substitution to explicit substitution (deduction version of sbieh 1764). New proofs should use sbied 1762 instead. (Contributed by NM, 30-Jun-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sbiedh.1 |
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sbiedh.2 |
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sbiedh.3 |
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Ref | Expression |
---|---|
sbiedh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb1 1740 |
. . . 4
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2 | sbiedh.1 |
. . . . 5
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3 | sbiedh.3 |
. . . . . . 7
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4 | bi1 117 |
. . . . . . 7
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5 | 3, 4 | syl6 33 |
. . . . . 6
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6 | 5 | impd 252 |
. . . . 5
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7 | 2, 6 | eximdh 1591 |
. . . 4
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8 | 1, 7 | syl5 32 |
. . 3
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9 | sbiedh.2 |
. . . 4
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10 | 2, 9 | 19.9hd 1641 |
. . 3
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11 | 8, 10 | syld 45 |
. 2
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12 | bi2 129 |
. . . . . . 7
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13 | 3, 12 | syl6 33 |
. . . . . 6
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14 | 13 | com23 78 |
. . . . 5
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15 | 2, 14 | alimdh 1444 |
. . . 4
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16 | sb2 1741 |
. . . 4
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17 | 15, 16 | syl6 33 |
. . 3
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18 | 9, 17 | syld 45 |
. 2
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19 | 11, 18 | 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-sb 1737 |
This theorem is referenced by: sbied 1762 sbieh 1764 sbcomxyyz 1946 |
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