Description: Obsolete version of hban as of 22-Oct-2026. (Contributed by NM, 14-May-1993) (Proof shortened by Wolf Lammen, 2-Jan-2018) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | hbOLD.1 | |- ( ph -> A. x ph ) |
|
| hbOLD.2 | |- ( ps -> A. x ps ) |
||
| Assertion | hbanOLD | |- ( ( ph /\ ps ) -> A. x ( ph /\ ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbOLD.1 | |- ( ph -> A. x ph ) |
|
| 2 | hbOLD.2 | |- ( ps -> A. x ps ) |
|
| 3 | 1 | nf5i | |- F/ x ph |
| 4 | 2 | nf5i | |- F/ x ps |
| 5 | 3 4 | nfan | |- F/ x ( ph /\ ps ) |
| 6 | 5 | nf5ri | |- ( ( ph /\ ps ) -> A. x ( ph /\ ps ) ) |