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Theorem rmoxfrd 27964
 Description: Transfer "at most one" restricted quantification from a variable to another variable contained in expression . (Contributed by Thierry Arnoux, 7-Apr-2017.) (Revised by Thierry Arnoux, 8-Oct-2017.)
Hypotheses
Ref Expression
rmoxfrd.1
rmoxfrd.2
rmoxfrd.3
Assertion
Ref Expression
rmoxfrd
Distinct variable groups:   ,   ,,   ,,   ,,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rmoxfrd
StepHypRef Expression
1 rmoxfrd.1 . . . . . 6
2 rmoxfrd.2 . . . . . . 7
3 reurex 3052 . . . . . . 7
42, 3syl 17 . . . . . 6
5 rmoxfrd.3 . . . . . 6
61, 4, 5rexxfrd 4637 . . . . 5
7 df-rex 2788 . . . . 5
8 df-rex 2788 . . . . 5
96, 7, 83bitr3g 290 . . . 4
101, 2, 5reuxfr4d 27961 . . . . 5
11 df-reu 2789 . . . . 5
12 df-reu 2789 . . . . 5
1310, 11, 123bitr3g 290 . . . 4
149, 13imbi12d 321 . . 3
15 df-mo 2271 . . 3
16 df-mo 2271 . . 3
1714, 15, 163bitr4g 291 . 2
18 df-rmo 2790 . 2
19 df-rmo 2790 . 2
2017, 18, 193bitr4g 291 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wex 1659   wcel 1870  weu 2266  wmo 2267  wrex 2783  wreu 2784  wrmo 2785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-reu 2789  df-rmo 2790  df-v 3089 This theorem is referenced by:  disjrdx  28040
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