Description: Commutative law for equality. Equality is a symmetric relation. Lemma 3 of KalishMontague p. 85. See also Lemma 7 of Tarski p. 69. (Contributed by NM, 10-Jan-1993) (Revised by NM, 9-Apr-2017)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | equcomi | |- ( x = y -> y = x ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equid | |- x = x |
|
| 2 | ax7 | |- ( x = y -> ( x = x -> y = x ) ) |
|
| 3 | 1 2 | mpi | |- ( x = y -> y = x ) |