Theorem nfcriiOLD

Description: Obsolete version of nfcrii as of 23-May-2024. (Contributed by Mario Carneiro, 11-Aug-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	nfcriOLD.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfcriiOLD	$$⊢y\in A\to \forall xy\in A$$

Proof

Step	Hyp	Ref	Expression
1		nfcriOLD.1	$$⊢\underset{\_}{Ⅎ}xA$$
2	1	nfcri	$$⊢Ⅎxz\in A$$
3	2	nfsbv	$$⊢Ⅎx\left[y/z\right]z\in A$$
4	3	nf5ri	$$⊢\left[y/z\right]z\in A\to \forall x\left[y/z\right]z\in A$$
5		clelsb1	$$⊢\left[y/z\right]z\in A\leftrightarrow y\in A$$
6	5	albii	$$⊢\forall x\left[y/z\right]z\in A\leftrightarrow \forall xy\in A$$
7	4 5 6	3imtr3i	$$⊢y\in A\to \forall xy\in A$$