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Mirrors > Home > ILE Home > Th. List > sbhypf | Unicode version |
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf . (Contributed by Raph Levien, 10-Apr-2004.) |
Ref | Expression |
---|---|
sbhypf.1 |
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sbhypf.2 |
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Ref | Expression |
---|---|
sbhypf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2554 |
. . 3
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2 | eqeq1 2043 |
. . 3
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3 | 1, 2 | ceqsexv 2587 |
. 2
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4 | nfs1v 1812 |
. . . 4
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5 | sbhypf.1 |
. . . 4
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6 | 4, 5 | nfbi 1478 |
. . 3
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7 | sbequ12 1651 |
. . . . 5
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8 | 7 | bicomd 129 |
. . . 4
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9 | sbhypf.2 |
. . . 4
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10 | 8, 9 | sylan9bb 435 |
. . 3
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11 | 6, 10 | exlimi 1482 |
. 2
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12 | 3, 11 | sylbir 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: mob2 2715 tfisi 4253 ralxpf 4425 rexxpf 4426 nn0ind-raph 8131 |
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