Description: Obsolete version of clel4 as of 1-Sep-2024. (Contributed by NM, 18-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | clel4.1 | |- B e. _V |
|
| Assertion | clel4OLD | |- ( A e. B <-> A. x ( x = B -> A e. x ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | clel4.1 | |- B e. _V |
|
| 2 | eleq2 | |- ( x = B -> ( A e. x <-> A e. B ) ) |
|
| 3 | 1 2 | ceqsalv | |- ( A. x ( x = B -> A e. x ) <-> A e. B ) |
| 4 | 3 | bicomi | |- ( A e. B <-> A. x ( x = B -> A e. x ) ) |