Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbceqal | Unicode version |
Description: A variation of extensionality for classes. (Contributed by Andrew Salmon, 28-Jun-2011.) |
Ref | Expression |
---|---|
sbceqal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spsbc 2920 | . 2 | |
2 | sbcimg 2950 | . . 3 | |
3 | eqid 2139 | . . . . 5 | |
4 | eqsbc3 2948 | . . . . 5 | |
5 | 3, 4 | mpbiri 167 | . . . 4 |
6 | pm5.5 241 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | eqsbc3 2948 | . . 3 | |
9 | 2, 7, 8 | 3bitrd 213 | . 2 |
10 | 1, 9 | sylibd 148 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 wsbc 2909 |
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-v 2688 df-sbc 2910 |
This theorem is referenced by: sbeqalb 2965 snsssn 3688 |
Copyright terms: Public domain | W3C validator |