Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eqsbc3 | Unicode version |
Description: Substitution applied to an atomic wff. Set theory version of eqsb3 2141. (Contributed by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
eqsbc3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 2766 | . 2 | |
2 | eqeq1 2046 | . 2 | |
3 | sbsbc 2768 | . . 3 | |
4 | eqsb3 2141 | . . 3 | |
5 | 3, 4 | bitr3i 175 | . 2 |
6 | 1, 2, 5 | vtoclbg 2614 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 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: sbceqal 2814 eqsbc3r 2819 |
Copyright terms: Public domain | W3C validator |