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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 2735 for class substitution version. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
csbhypf.1 | |
csbhypf.2 | |
csbhypf.3 |
Ref | Expression |
---|---|
csbhypf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbhypf.1 | . . . 4 | |
2 | 1 | nfeq2 2293 | . . 3 |
3 | nfcsb1v 3035 | . . . 4 | |
4 | csbhypf.2 | . . . 4 | |
5 | 3, 4 | nfeq 2289 | . . 3 |
6 | 2, 5 | nfim 1551 | . 2 |
7 | eqeq1 2146 | . . 3 | |
8 | csbeq1a 3012 | . . . 4 | |
9 | 8 | eqeq1d 2148 | . . 3 |
10 | 7, 9 | imbi12d 233 | . 2 |
11 | csbhypf.3 | . 2 | |
12 | 6, 10, 11 | chvar 1730 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wnfc 2268 csb 3003 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: disji2 3922 tfisi 4501 |
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