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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 1790). New proofs should use sbied 1788 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 1766 |
. . . 4
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2 | sbiedh.1 |
. . . . 5
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3 | sbiedh.3 |
. . . . . . 7
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4 | biimp 118 |
. . . . . . 7
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5 | 3, 4 | syl6 33 |
. . . . . 6
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6 | 5 | impd 254 |
. . . . 5
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7 | 2, 6 | eximdh 1611 |
. . . 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 1662 |
. . 3
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11 | 8, 10 | syld 45 |
. 2
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12 | biimpr 130 |
. . . . . . 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 1467 |
. . . 4
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16 | sb2 1767 |
. . . 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 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 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: sbied 1788 sbieh 1790 sbcomxyyz 1972 |
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