Theorem fvilbdRP

Description: A set is a subset of its image under the identity relation. (Contributed by RP, 22-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	fvilbdRP.r	|- ( ph -> R e. _V )
Assertion	fvilbdRP	|- ( ph -> R C_ ( _I ` R ) )

Proof

Step	Hyp	Ref	Expression
1		fvilbdRP.r	|- ( ph -> R e. _V )
2		dfid6	|- _I = ( r e. _V |-> U_ n e. { 1 } ( r ^r n ) )
3		snex	|- { 1 } e. _V
4	3	a1i	|- ( ph -> { 1 } e. _V )
5		1ex	|- 1 e. _V
6	5	snid	|- 1 e. { 1 }
7	6	a1i	|- ( ph -> 1 e. { 1 } )
8	2 1 4 7	fvmptiunrelexplb1d	|- ( ph -> R C_ ( _I ` R ) )