Theorem sn-rediv1d

Description: A number divided by 1 is itself. (Contributed by SN, 2-Apr-2026)

	Ref	Expression
Hypothesis	sn-rediv1d.a	|- ( ph -> A e. RR )
Assertion	sn-rediv1d	|- ( ph -> ( A /R 1 ) = A )

Proof

Step	Hyp	Ref	Expression
1		sn-rediv1d.a	|- ( ph -> A e. RR )
2		remullid	|- ( A e. RR -> ( 1 x. A ) = A )
3	1 2	syl	|- ( ph -> ( 1 x. A ) = A )
4		1red	|- ( ph -> 1 e. RR )
5		ax-1ne0	|- 1 =/= 0
6	5	a1i	|- ( ph -> 1 =/= 0 )
7	1 1 4 6	redivmuld	|- ( ph -> ( ( A /R 1 ) = A <-> ( 1 x. A ) = A ) )
8	3 7	mpbird	|- ( ph -> ( A /R 1 ) = A )