Description: Partially closed form of sbtr . Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by BJ, 4-Jun-2019) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbtrt.nf | |- F/ y ph |
|
| Assertion | sbtrt | |- ( A. y [ y / x ] ph -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbtrt.nf | |- F/ y ph |
|
| 2 | stdpc4 | |- ( A. y [ y / x ] ph -> [ x / y ] [ y / x ] ph ) |
|
| 3 | 1 | sbid2 | |- ( [ x / y ] [ y / x ] ph <-> ph ) |
| 4 | 2 3 | sylib | |- ( A. y [ y / x ] ph -> ph ) |