Description: Obsolete version of hb3an as of 23-Oct-2026. (Contributed by NM, 14-Sep-2003) (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 ) |
||
| hbOLD.3 | |- ( ch -> A. x ch ) |
||
| Assertion | hb3anOLD | |- ( ( ph /\ ps /\ ch ) -> A. x ( ph /\ ps /\ ch ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbOLD.1 | |- ( ph -> A. x ph ) |
|
| 2 | hbOLD.2 | |- ( ps -> A. x ps ) |
|
| 3 | hbOLD.3 | |- ( ch -> A. x ch ) |
|
| 4 | 1 | nf5i | |- F/ x ph |
| 5 | 2 | nf5i | |- F/ x ps |
| 6 | 3 | nf5i | |- F/ x ch |
| 7 | 4 5 6 | nf3an | |- F/ x ( ph /\ ps /\ ch ) |
| 8 | 7 | nf5ri | |- ( ( ph /\ ps /\ ch ) -> A. x ( ph /\ ps /\ ch ) ) |