Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > clel4 | Unicode version |
Description: An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
clel4.1 |
Ref | Expression |
---|---|
clel4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clel4.1 | . . 3 | |
2 | eleq2 2221 | . . 3 | |
3 | 1, 2 | ceqsalv 2742 | . 2 |
4 | 3 | bicomi 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 wceq 1335 wcel 2128 cvv 2712 |
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-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 |
This theorem is referenced by: intpr 3839 |
Copyright terms: Public domain | W3C validator |