Theorem ensymb

Description: Symmetry of equinumerosity. Theorem 2 of Suppes p. 92. (Contributed by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	ensymb	$$⊢A\approx B\leftrightarrow B\approx A$$

Proof

Step	Hyp	Ref	Expression
1		ener	$$⊢\approx \mathrm{Er}\mathrm{V}$$
2	1	a1i	$$⊢\top \to \approx \mathrm{Er}\mathrm{V}$$
3	2	ersymb	$$⊢\top \to \left(A\approx B\leftrightarrow B\approx A\right)$$
4	3	mptru	$$⊢A\approx B\leftrightarrow B\approx A$$