Theorem sb3OLD

Description: Obsolete version of sb3 as of 21-Feb-2024. (Contributed by NM, 5-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sb3OLD	$$⊢\neg \forall xx=y\to \left(\exists x\left(x=y\wedge \phi \right)\to \left[y/x\right]\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		equs5	$$⊢\neg \forall xx=y\to \left(\exists x\left(x=y\wedge \phi \right)\leftrightarrow \forall x\left(x=y\to \phi \right)\right)$$
2		sb2	$$⊢\forall x\left(x=y\to \phi \right)\to \left[y/x\right]\phi$$
3	1 2	syl6bi	$$⊢\neg \forall xx=y\to \left(\exists x\left(x=y\wedge \phi \right)\to \left[y/x\right]\phi \right)$$