Definition df-rmo 2480

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 2475	. 2 wff ∃*𝑥 ∈ 𝐴 𝜑
5	2	cv 1363	. . . . 5 class 𝑥
6	5, 3	wcel 2164	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 104	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	wmo 2043	. 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  2667  rmobida  2681  rmobiia  2684  rmoeq1f  2689  mormo  2710  reu5  2711  rmo5  2714  rmov  2780  rmo4  2954  rmo3f  2958  rmoan  2961  rmoim  2962  rmoimi2  2964  2reuswapdc  2965  2rmorex  2967  rmo2ilem  3076  rmo3  3078  rmob  3079  ssrmof  3243  dfdisj2  4009  dffun9  5284  fncnv  5321