Theorem fvrtrcllb1d

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

	Ref	Expression
Hypothesis	fvrtrcllb1d.r	|- ( ph -> R e. _V )
Assertion	fvrtrcllb1d	|- ( ph -> R C_ ( t* ` R ) )

Proof

Step	Hyp	Ref	Expression
1		fvrtrcllb1d.r	|- ( ph -> R e. _V )
2		dfrtrcl3	|- t* = ( r e. _V |-> U_ n e. NN0 ( r ^r n ) )
3		nn0ex	|- NN0 e. _V
4	3	a1i	|- ( ph -> NN0 e. _V )
5		1nn0	|- 1 e. NN0
6	5	a1i	|- ( ph -> 1 e. NN0 )
7	2 1 4 6	fvmptiunrelexplb1d	|- ( ph -> R C_ ( t* ` R ) )