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Theorem 2rmorex 3304
Description: Double restricted quantification with "at most one," analogous to 2moex 2365. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
2rmorex
Distinct variable groups:   ,   ,   ,

Proof of Theorem 2rmorex
StepHypRef Expression
1 nfcv 2619 . . 3
2 nfre1 2918 . . 3
31, 2nfrmo 3033 . 2
4 rspe 2915 . . . . . 6
54ex 434 . . . . 5
65ralrimivw 2872 . . . 4
7 rmoim 3299 . . . 4
86, 7syl 16 . . 3
98com12 31 . 2
103, 9ralrimi 2857 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  E.wrex 2808  E*wrmo 2810
This theorem is referenced by:  2reu2  32192
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rmo 2815
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