Description: If y is not free in ph , x is not free in [ y / x ] ph . Usage of this theorem is discouraged because it depends on ax-13 . Check out bj-hbsb3v for a weaker version requiring less axioms. (Contributed by NM, 14-May-1993) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | hbsb3.1 | |- ( ph -> A. y ph ) |
|
| Assertion | hbsb3 | |- ( [ y / x ] ph -> A. x [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbsb3.1 | |- ( ph -> A. y ph ) |
|
| 2 | 1 | sbimi | |- ( [ y / x ] ph -> [ y / x ] A. y ph ) |
| 3 | hbsb2a | |- ( [ y / x ] A. y ph -> A. x [ y / x ] ph ) |
|
| 4 | 2 3 | syl | |- ( [ y / x ] ph -> A. x [ y / x ] ph ) |