Description: Special case of a bound-variable hypothesis builder for substitution. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Feb-2007) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | hbsb2a | |- ( [ y / x ] A. y ph -> A. x [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sb4a | |- ( [ y / x ] A. y ph -> A. x ( x = y -> ph ) ) |
|
| 2 | sb2 | |- ( A. x ( x = y -> ph ) -> [ y / x ] ph ) |
|
| 3 | 2 | axc4i | |- ( A. x ( x = y -> ph ) -> A. x [ y / x ] ph ) |
| 4 | 1 3 | syl | |- ( [ y / x ] A. y ph -> A. x [ y / x ] ph ) |