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Theorem Delete

⊦ a ∈ s -- b ↔ a ≠ b ∧ a ∈ s

Type: An axiom
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: add-inter-rem, add-rem-sub, del, del-addeq, del-addeq-01, del-addeq-02, del-addeq-03, del-addeq-04, del-addeq-05, del-addeq-06, del-addin-01, del-d, del-d-01, del-del-one, del-e, del-e-01, del-e-02, del-eq, del-feq, del-feq-01, del-feq-02, del-in, del-in-01, del-in-02, del-in-03, del-neq-01, del-neq-02, del-notin, del-two, delete-insert, delete-shift, delete-subset, delsw, delsw-01, delsw-02, delsw-suc, diff-add-del, diff-del, diff-del-01, diff-del-02, diff-del-minus, diff-del-minus-2, diff-del-minus-3, diff-subset-01, equal-add-in, indef, insdel-sub, int-del-rew, int-notempty-01, intdel-empty, intersect-add-rem, intersect-empty-rem, k-delete-rec, k-diff-rec1, k-intersect-rec1, k-intersect-rec2, rem-union-ins, sub-ade, sub-ade-01, sub-ade-02, sub-ade-03, sub-del, sub-del-01, sub-del-02, sub-del-03, sub-del-04, sub-del-05, sub-rem-inter-rem, subset-del, subseteq-rem-del, subsub-del, undel, undel-01, undel-02, undel-04, undel-06, unindel, uninsubdel, union-del, union-rem-add, union-rem-unchdg, unsubdel, unsubdel-01,
Used by units in proved state:
Proof exists?: No