Theorem permsetexOLD

Description: Obsolete version of f1osetex as of 8-Aug-2024. (Contributed by AV, 30-Mar-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	permsetexOLD	$$⊢A\in V\to \left\{f|f:A\underset{1-1\; onto}{⟶}A\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		mapex	$$⊢\left(A\in V\wedge A\in V\right)\to \left\{f|f:A⟶A\right\}\in \mathrm{V}$$
2	1	anidms	$$⊢A\in V\to \left\{f|f:A⟶A\right\}\in \mathrm{V}$$
3		f1of	$$⊢f:A\underset{1-1\; onto}{⟶}A\to f:A⟶A$$
4	3	ss2abi	$$⊢\left\{f|f:A\underset{1-1\; onto}{⟶}A\right\}\subseteq \left\{f|f:A⟶A\right\}$$
5	4	a1i	$$⊢A\in V\to \left\{f|f:A\underset{1-1\; onto}{⟶}A\right\}\subseteq \left\{f|f:A⟶A\right\}$$
6	2 5	ssexd	$$⊢A\in V\to \left\{f|f:A\underset{1-1\; onto}{⟶}A\right\}\in \mathrm{V}$$