Description: Bound-variable hypothesis builder for restricted quantification. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfralw when possible. (Contributed by NM, 1-Sep-1999) (Revised by Mario Carneiro, 7-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfral.1 | |- F/_ x A |
|
| nfral.2 | |- F/ x ph |
||
| Assertion | nfral | |- F/ x A. y e. A ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfral.1 | |- F/_ x A |
|
| 2 | nfral.2 | |- F/ x ph |
|
| 3 | nftru | |- F/ y T. |
|
| 4 | 1 | a1i | |- ( T. -> F/_ x A ) |
| 5 | 2 | a1i | |- ( T. -> F/ x ph ) |
| 6 | 3 4 5 | nfrald | |- ( T. -> F/ x A. y e. A ph ) |
| 7 | 6 | mptru | |- F/ x A. y e. A ph |