Definition df-rmo 2463

Description: Define restricted "at most one". (Contributed by NM, 16-Jun-2017.)

Assertion

Ref	Expression
df-rmo	⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

Detailed syntax breakdown of Definition df-rmo

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		vx	. . 3 setvar 𝑥
3		cA	. . 3 class 𝐴
4	1, 2, 3	wrmo 2458	. 2 wff ∃*𝑥 ∈ 𝐴 𝜑
5	2	cv 1352	. . . . 5 class 𝑥
6	5, 3	wcel 2148	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 104	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	wmo 2027	. 2 wff ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)
9	4, 8	wb 105	1 wff (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  nfrmo1  2649  rmobida  2663  rmobiia  2666  rmoeq1f  2671  mormo  2688  reu5  2689  rmo5  2692  rmov  2757  rmo4  2930  rmo3f  2934  rmoan  2937  rmoim  2938  rmoimi2  2940  2reuswapdc  2941  2rmorex  2943  rmo2ilem  3052  rmo3  3054  rmob  3055  ssrmof  3218  dfdisj2  3982  dffun9  5245  fncnv  5282