Theorem sb6rfv

Description: Reversed substitution. Version of sb6rf requiring disjoint variables, but fewer axioms. (Contributed by NM, 1-Aug-1993) (Revised by Wolf Lammen, 7-Feb-2023)

	Ref	Expression
Hypothesis	sb6rfv.nf	$$⊢Ⅎy\phi$$
Assertion	sb6rfv	$$⊢\phi \leftrightarrow \forall y\left(y=x\to \left[y/x\right]\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sb6rfv.nf	$$⊢Ⅎy\phi$$
2		sbequ12r	$$⊢y=x\to \left(\left[y/x\right]\phi \leftrightarrow \phi \right)$$
3	1 2	equsalv	$$⊢\forall y\left(y=x\to \left[y/x\right]\phi \right)\leftrightarrow \phi$$
4	3	bicomi	$$⊢\phi \leftrightarrow \forall y\left(y=x\to \left[y/x\right]\phi \right)$$