Description: Theorem 19.21 of Margaris p. 90. The hypothesis can be thought of as " x is not free in ph ". See also 19.21 and 19.21v . (Contributed by NM, 1-Aug-2017) (Proof shortened by Wolf Lammen, 1-Jan-2018)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | 19.21h.1 | |- ( ph -> A. x ph ) |
|
| Assertion | 19.21h | |- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.21h.1 | |- ( ph -> A. x ph ) |
|
| 2 | 1 | nf5i | |- F/ x ph |
| 3 | 2 | 19.21 | |- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) |