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Theorem 2rmorex 2982
 Description: Double restricted quantification with "at most one," analogous to 2moex 2227. (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 2432 . . 3
2 nfre1 2612 . . 3
31, 2nfrmo 2728 . 2
4 rspe 2617 . . . . . 6
54ex 423 . . . . 5
65ralrimivw 2640 . . . 4
7 rmoim 2977 . . . 4
86, 7syl 15 . . 3
98com12 27 . 2
103, 9ralrimi 2637 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1696  wral 2556  wrex 2557  wrmo 2559 This theorem is referenced by:  2reu2  28068 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rmo 2564
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