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Theorem 2rmorex 3040
 Description: Double restricted quantification with "at most one," analogous to 2moex 2275. (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 2489 . . 3
2 nfre1 2670 . . 3
31, 2nfrmo 2786 . 2
4 rspe 2675 . . . . . 6
54ex 423 . . . . 5
65ralrimivw 2698 . . . 4
7 rmoim 3035 . . . 4
86, 7syl 15 . . 3
98com12 27 . 2
103, 9ralrimi 2695 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1710  wral 2614  wrex 2615  wrmo 2617 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-rmo 2622 This theorem is referenced by: (None)
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