New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > pm13.183 | Unicode version |
Description: Compare theorem *13.183 in [WhiteheadRussell] p. 178. Only is required to be a set. (Contributed by Andrew Salmon, 3-Jun-2011.) |
Ref | Expression |
---|---|
pm13.183 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2359 | . 2 | |
2 | eqeq2 2362 | . . . 4 | |
3 | 2 | bibi1d 310 | . . 3 |
4 | 3 | albidv 1625 | . 2 |
5 | eqeq2 2362 | . . . 4 | |
6 | 5 | alrimiv 1631 | . . 3 |
7 | stdpc4 2024 | . . . 4 | |
8 | sbbi 2071 | . . . . 5 | |
9 | eqsb3 2454 | . . . . . . 7 | |
10 | 9 | bibi2i 304 | . . . . . 6 |
11 | equsb1 2034 | . . . . . . 7 | |
12 | bi1 178 | . . . . . . 7 | |
13 | 11, 12 | mpi 16 | . . . . . 6 |
14 | 10, 13 | sylbi 187 | . . . . 5 |
15 | 8, 14 | sylbi 187 | . . . 4 |
16 | 7, 15 | syl 15 | . . 3 |
17 | 6, 16 | impbii 180 | . 2 |
18 | 1, 4, 17 | vtoclbg 2915 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wal 1540 wceq 1642 wsb 1648 wcel 1710 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |