Description: Alternate proof of axc16 , shorter but requiring ax-10 , ax-11 , ax-13 and using df-nf and df-sb . (Contributed by NM, 17-May-2008) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | axc16ALT | |- ( A. x x = y -> ( ph -> A. x ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbequ12 | |- ( x = z -> ( ph <-> [ z / x ] ph ) ) |
|
| 2 | ax-5 | |- ( ph -> A. z ph ) |
|
| 3 | 2 | hbsb3 | |- ( [ z / x ] ph -> A. x [ z / x ] ph ) |
| 4 | 1 3 | axc16i | |- ( A. x x = y -> ( ph -> A. x ph ) ) |