Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  2rmorex Structured version   Unicode version

Theorem 2rmorex 3140
 Description: Double restricted quantification with "at most one," analogous to 2moex 2354. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
2rmorex
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem 2rmorex
StepHypRef Expression
1 nfcv 2574 . . 3
2 nfre1 2764 . . 3
31, 2nfrmo 2885 . 2
4 rspe 2769 . . . . . 6
54ex 425 . . . . 5
65ralrimivw 2792 . . . 4
7 rmoim 3135 . . . 4
86, 7syl 16 . . 3
98com12 30 . 2
103, 9ralrimi 2789 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1726  wral 2707  wrex 2708  wrmo 2710 This theorem is referenced by:  2reu2  27943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rmo 2715
 Copyright terms: Public domain W3C validator