Theorem sbtrt

Description: Partially closed form of sbtr . Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by BJ, 4-Jun-2019) (New usage is discouraged.)

	Ref	Expression
Hypothesis	sbtrt.nf	$$⊢Ⅎy\phi$$
Assertion	sbtrt	$$⊢\forall y\left[y/x\right]\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		sbtrt.nf	$$⊢Ⅎy\phi$$
2		stdpc4	$$⊢\forall y\left[y/x\right]\phi \to \left[x/y\right]\left[y/x\right]\phi$$
3	1	sbid2	$$⊢\left[x/y\right]\left[y/x\right]\phi \leftrightarrow \phi$$
4	2 3	sylib	$$⊢\forall y\left[y/x\right]\phi \to \phi$$