Theorem wl-ax11-lem5

Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019)

	Ref	Expression
Assertion	wl-ax11-lem5	$$⊢\forall uu=y\to \left(\forall u\left[u/y\right]\phi \leftrightarrow \forall y\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbequ12r	$$⊢u=y\to \left(\left[u/y\right]\phi \leftrightarrow \phi \right)$$
2	1	sps	$$⊢\forall uu=y\to \left(\left[u/y\right]\phi \leftrightarrow \phi \right)$$
3	2	dral1	$$⊢\forall uu=y\to \left(\forall u\left[u/y\right]\phi \leftrightarrow \forall y\phi \right)$$