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Mirrors > Home > ILE Home > Th. List > csbhypf | Unicode version |
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See sbhypf 2738 for class substitution version. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
csbhypf.1 |
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csbhypf.2 |
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csbhypf.3 |
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Ref | Expression |
---|---|
csbhypf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbhypf.1 |
. . . 4
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2 | 1 | nfeq2 2294 |
. . 3
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3 | nfcsb1v 3040 |
. . . 4
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4 | csbhypf.2 |
. . . 4
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5 | 3, 4 | nfeq 2290 |
. . 3
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6 | 2, 5 | nfim 1552 |
. 2
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7 | eqeq1 2147 |
. . 3
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8 | csbeq1a 3016 |
. . . 4
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9 | 8 | eqeq1d 2149 |
. . 3
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10 | 7, 9 | imbi12d 233 |
. 2
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11 | csbhypf.3 |
. 2
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12 | 6, 10, 11 | chvar 1731 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-sbc 2914 df-csb 3008 |
This theorem is referenced by: disji2 3930 tfisi 4509 |
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