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Theorem rmoxfrdOLD 28004
 Description: Transfer "at most one" restricted quantification from a variable to another variable contained in expression . (Contributed by Thierry Arnoux, 7-Apr-2017.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
rmoxfrd.1
rmoxfrd.2
rmoxfrd.3
Assertion
Ref Expression
rmoxfrdOLD
Distinct variable groups:   ,   ,,   ,,   ,,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rmoxfrdOLD
StepHypRef Expression
1 rmoxfrd.1 . . . . 5
2 rmoxfrd.2 . . . . . 6
3 reurex 3043 . . . . . 6
42, 3syl 17 . . . . 5
5 rmoxfrd.3 . . . . 5
61, 4, 5rexxfrd 4628 . . . 4
7 df-rex 2779 . . . 4
8 df-rex 2779 . . . 4
96, 7, 83bitr3g 290 . . 3
101, 2, 5reuxfr4d 28002 . . . 4
11 df-reu 2780 . . . 4
12 df-reu 2780 . . . 4
1310, 11, 123bitr3g 290 . . 3
149, 13imbi12d 321 . 2
15 df-mo 2268 . 2
16 df-mo 2268 . 2
1714, 15, 163bitr4g 291 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wex 1659   wcel 1867  weu 2263  wmo 2264  wrex 2774  wreu 2775 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 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 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 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ral 2778  df-rex 2779  df-reu 2780  df-rmo 2781  df-v 3080 This theorem is referenced by: (None)
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