Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of KalishMontague p. 86. (Contributed by Wolf Lammen, 5-Mar-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | wl-cbvmotv | |- ( E* x T. -> E* y T. ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax7v2 | |- ( x = y -> ( x = z -> y = z ) ) |
|
| 2 | 1 | imim2d | |- ( x = y -> ( ( T. -> x = z ) -> ( T. -> y = z ) ) ) |
| 3 | 2 | cbvalivw | |- ( A. x ( T. -> x = z ) -> A. y ( T. -> y = z ) ) |
| 4 | 3 | eximi | |- ( E. z A. x ( T. -> x = z ) -> E. z A. y ( T. -> y = z ) ) |
| 5 | df-mo | |- ( E* x T. <-> E. z A. x ( T. -> x = z ) ) |
|
| 6 | df-mo | |- ( E* y T. <-> E. z A. y ( T. -> y = z ) ) |
|
| 7 | 4 5 6 | 3imtr4i | |- ( E* x T. -> E* y T. ) |