Description: Obsolete version of ssralv as of 19-May-2025. (Contributed by NM, 11-Mar-2006) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ssralvOLD | |- ( A C_ B -> ( A. x e. B ph -> A. x e. A ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssel | |- ( A C_ B -> ( x e. A -> x e. B ) ) |
|
| 2 | 1 | imim1d | |- ( A C_ B -> ( ( x e. B -> ph ) -> ( x e. A -> ph ) ) ) |
| 3 | 2 | ralimdv2 | |- ( A C_ B -> ( A. x e. B ph -> A. x e. A ph ) ) |