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 | hbsb2e | |- ( [ y / x ] ph -> A. x [ y / x ] E. y ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb4e | |- ( [ y / x ] ph -> A. x ( x = y -> E. y ph ) ) |
|
2 | sb2 | |- ( A. x ( x = y -> E. y ph ) -> [ y / x ] E. y ph ) |
|
3 | 2 | axc4i | |- ( A. x ( x = y -> E. y ph ) -> A. x [ y / x ] E. y ph ) |
4 | 1 3 | syl | |- ( [ y / x ] ph -> A. x [ y / x ] E. y ph ) |