Theorem eqcomd

Description: Deduction from commutative law for class equality. (Contributed by NM, 15-Aug-1994) Allow shortening of eqcom . (Revised by Wolf Lammen, 19-Nov-2019)

	Ref	Expression
Hypothesis	eqcomd.1	$$⊢\phi \to A=B$$
Assertion	eqcomd	$$⊢\phi \to B=A$$

Proof

Step	Hyp	Ref	Expression
1		eqcomd.1	$$⊢\phi \to A=B$$
2		eqid	$$⊢A=A$$
3	1	eqeq1d	$$⊢\phi \to \left(A=A\leftrightarrow B=A\right)$$
4	2 3	mpbii	$$⊢\phi \to B=A$$