Theorem rerecrecd

Description: A number is equal to the reciprocal of its reciprocal. (Contributed by SN, 2-Apr-2026)

	Ref	Expression
Hypotheses	sn-rereccld.a	$$⊢\phi \to A\in ℝ$$
	sn-rereccld.z	$$⊢\phi \to A\ne 0$$
Assertion	rerecrecd	Could not format assertion : No typesetting found for |- ( ph -> ( 1 /R ( 1 /R A ) ) = A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	$$⊢\phi \to A\in ℝ$$
2		sn-rereccld.z	$$⊢\phi \to A\ne 0$$
3	1 2	rerecid2d	Could not format ( ph -> ( ( 1 /R A ) x. A ) = 1 ) : No typesetting found for |- ( ph -> ( ( 1 /R A ) x. A ) = 1 ) with typecode |-
4		1red	$$⊢\phi \to 1\in ℝ$$
5	1 2	sn-rereccld	Could not format ( ph -> ( 1 /R A ) e. RR ) : No typesetting found for |- ( ph -> ( 1 /R A ) e. RR ) with typecode |-
6	1 2	rerecne0d	Could not format ( ph -> ( 1 /R A ) =/= 0 ) : No typesetting found for |- ( ph -> ( 1 /R A ) =/= 0 ) with typecode |-
7	4 1 5 6	redivmuld	Could not format ( ph -> ( ( 1 /R ( 1 /R A ) ) = A <-> ( ( 1 /R A ) x. A ) = 1 ) ) : No typesetting found for |- ( ph -> ( ( 1 /R ( 1 /R A ) ) = A <-> ( ( 1 /R A ) x. A ) = 1 ) ) with typecode |-
8	3 7	mpbird	Could not format ( ph -> ( 1 /R ( 1 /R A ) ) = A ) : No typesetting found for |- ( ph -> ( 1 /R ( 1 /R A ) ) = A ) with typecode |-