Theorem wl-equsalcom

Description: This simple equivalence eases substitution of one expression for the other. (Contributed by Wolf Lammen, 1-Sep-2018)

	Ref	Expression
Assertion	wl-equsalcom	$$⊢\forall x\left(x=y\to \phi \right)\leftrightarrow \forall x\left(y=x\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		equcom	$$⊢x=y\leftrightarrow y=x$$
2	1	imbi1i	$$⊢\left(x=y\to \phi \right)\leftrightarrow \left(y=x\to \phi \right)$$
3	2	albii	$$⊢\forall x\left(x=y\to \phi \right)\leftrightarrow \forall x\left(y=x\to \phi \right)$$