Theorem fvrcllb1d

Description: A set is a subset of its image under the reflexive closure. (Contributed by RP, 22-Jul-2020)

	Ref	Expression
Hypothesis	fvrcllb1d.r	|- ( ph -> R e. _V )
Assertion	fvrcllb1d	|- ( ph -> R C_ ( r* ` R ) )

Proof

Step	Hyp	Ref	Expression
1		fvrcllb1d.r	|- ( ph -> R e. _V )
2		dfrcl4	|- r* = ( r e. _V |-> U_ n e. { 0 , 1 } ( r ^r n ) )
3		prex	|- { 0 , 1 } e. _V
4	3	a1i	|- ( ph -> { 0 , 1 } e. _V )
5		1ex	|- 1 e. _V
6	5	prid2	|- 1 e. { 0 , 1 }
7	6	a1i	|- ( ph -> 1 e. { 0 , 1 } )
8	2 1 4 7	fvmptiunrelexplb1d	|- ( ph -> R C_ ( r* ` R ) )