Theorem elec

Description: Membership in an equivalence class. Theorem 72 of Suppes p. 82. (Contributed by NM, 23-Jul-1995)

	Ref	Expression
Hypotheses	elec.1	$$⊢A\in \mathrm{V}$$
	elec.2	$$⊢B\in \mathrm{V}$$
Assertion	elec	$$⊢A\in \left[B\right]R\leftrightarrow BRA$$

Proof

Step	Hyp	Ref	Expression
1		elec.1	$$⊢A\in \mathrm{V}$$
2		elec.2	$$⊢B\in \mathrm{V}$$
3		elecg	$$⊢\left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)\to \left(A\in \left[B\right]R\leftrightarrow BRA\right)$$
4	1 2 3	mp2an	$$⊢A\in \left[B\right]R\leftrightarrow BRA$$