Theorem fvtrcllb1d

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

	Ref	Expression
Hypothesis	fvtrcllb1d.r	|- ( ph -> R e. _V )
Assertion	fvtrcllb1d	|- ( ph -> R C_ ( t+ ` R ) )

Proof

Step	Hyp	Ref	Expression
1		fvtrcllb1d.r	|- ( ph -> R e. _V )
2		dftrcl3	|- t+ = ( r e. _V |-> U_ n e. NN ( r ^r n ) )
3		nnex	|- NN e. _V
4	3	a1i	|- ( ph -> NN e. _V )
5		1nn	|- 1 e. NN
6	5	a1i	|- ( ph -> 1 e. NN )
7	2 1 4 6	fvmptiunrelexplb1d	|- ( ph -> R C_ ( t+ ` R ) )