Description: Deduction version of bound-variable hypothesis builder nfov . (Contributed by NM, 13-Dec-2005) (Proof shortened by Andrew Salmon, 22-Oct-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfovd.2 | |- ( ph -> F/_ x A ) |
|
| nfovd.3 | |- ( ph -> F/_ x F ) |
||
| nfovd.4 | |- ( ph -> F/_ x B ) |
||
| Assertion | nfovd | |- ( ph -> F/_ x ( A F B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfovd.2 | |- ( ph -> F/_ x A ) |
|
| 2 | nfovd.3 | |- ( ph -> F/_ x F ) |
|
| 3 | nfovd.4 | |- ( ph -> F/_ x B ) |
|
| 4 | df-ov | |- ( A F B ) = ( F ` <. A , B >. ) |
|
| 5 | 1 3 | nfopd | |- ( ph -> F/_ x <. A , B >. ) |
| 6 | 2 5 | nffvd | |- ( ph -> F/_ x ( F ` <. A , B >. ) ) |
| 7 | 4 6 | nfcxfrd | |- ( ph -> F/_ x ( A F B ) ) |