Description: An identity law for substitution. Usage of this theorem is discouraged because it depends on ax-13 . Check out sbid2vw for a weaker version requiring fewer axioms. (Contributed by NM, 14-May-1993) (Revised by Mario Carneiro, 6-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbid2.1 | |- F/ x ph |
|
| Assertion | sbid2 | |- ( [ y / x ] [ x / y ] ph <-> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbid2.1 | |- F/ x ph |
|
| 2 | sbco | |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) |
|
| 3 | 1 | sbf | |- ( [ y / x ] ph <-> ph ) |
| 4 | 2 3 | bitri | |- ( [ y / x ] [ x / y ] ph <-> ph ) |