Description: Obsolete version of nfreuw as of 21-Nov-2024. (Contributed by NM, 30-Oct-2010) (Revised by GG, 10-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfreuwOLD.1 | |- F/_ x A |
|
| nfreuwOLD.2 | |- F/ x ph |
||
| Assertion | nfreuwOLD | |- F/ x E! y e. A ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfreuwOLD.1 | |- F/_ x A |
|
| 2 | nfreuwOLD.2 | |- F/ x ph |
|
| 3 | df-reu | |- ( E! y e. A ph <-> E! y ( y e. A /\ ph ) ) |
|
| 4 | nftru | |- F/ y T. |
|
| 5 | nfcvd | |- ( T. -> F/_ x y ) |
|
| 6 | 1 | a1i | |- ( T. -> F/_ x A ) |
| 7 | 5 6 | nfeld | |- ( T. -> F/ x y e. A ) |
| 8 | 2 | a1i | |- ( T. -> F/ x ph ) |
| 9 | 7 8 | nfand | |- ( T. -> F/ x ( y e. A /\ ph ) ) |
| 10 | 4 9 | nfeudw | |- ( T. -> F/ x E! y ( y e. A /\ ph ) ) |
| 11 | 3 10 | nfxfrd | |- ( T. -> F/ x E! y e. A ph ) |
| 12 | 11 | mptru | |- F/ x E! y e. A ph |