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Theorem rmoanim 27924
 Description: Introduction of a conjunct into restricted "at most one" quantifier, analogous to moanim 2336. (Contributed by Alexander van der Vekens, 25-Jun-2017.)
Hypothesis
Ref Expression
rmoanim.1
Assertion
Ref Expression
rmoanim
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rmoanim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 impexp 434 . . . . 5
21ralbii 2721 . . . 4
3 rmoanim.1 . . . . 5
43r19.21 2784 . . . 4
52, 4bitri 241 . . 3
65exbii 1592 . 2
7 nfv 1629 . . 3
87rmo2 3238 . 2
9 nfv 1629 . . . . 5
109rmo2 3238 . . . 4
1110imbi2i 304 . . 3
12 19.37v 1922 . . 3
1311, 12bitr4i 244 . 2
146, 8, 133bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553  wral 2697  wrmo 2700 This theorem is referenced by:  2reu1  27931 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-ral 2702  df-rmo 2705
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