Theorem dfcomember

Description: Alternate definition of the comember equivalence relation. (Contributed by Peter Mazsa, 28-Nov-2022)

	Ref	Expression
Assertion	dfcomember	Could not format assertion : No typesetting found for |- ( CoMembEr A <-> ~ A ErALTV A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		df-comember	Could not format ( CoMembEr A <-> ,~ ( `' _E |` A ) ErALTV A ) : No typesetting found for |- ( CoMembEr A <-> ,~ ( `' _E |` A ) ErALTV A ) with typecode |-
2		df-coels	$$⊢\sim A=\wr \left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)$$
3	2	erALTVeq1i	$$⊢\sim AErALTVA\leftrightarrow \wr \left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)ErALTVA$$
4	1 3	bitr4i	Could not format ( CoMembEr A <-> ~ A ErALTV A ) : No typesetting found for |- ( CoMembEr A <-> ~ A ErALTV A ) with typecode |-