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Mirrors > Home > ILE Home > Th. List > sbctt | Unicode version |
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
sbctt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq2 2767 | . . . . 5 | |
2 | 1 | bibi1d 222 | . . . 4 |
3 | 2 | imbi2d 219 | . . 3 |
4 | sbft 1728 | . . 3 | |
5 | 3, 4 | vtoclg 2613 | . 2 |
6 | 5 | imp 115 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wcel 1393 wsb 1645 wsbc 2764 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 |
This theorem is referenced by: sbcgf 2825 csbtt 2862 |
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