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Theorem rmoanim 32387
 Description: Introduction of a conjunct into restricted "at most one" quantifier, analogous to moanim 2350. (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 446 . . . . 5
21ralbii 2888 . . . 4
3 rmoanim.1 . . . . 5
43r19.21 2856 . . . 4
52, 4bitri 249 . . 3
65exbii 1668 . 2
7 nfv 1708 . . 3
87rmo2 3423 . 2
9 nfv 1708 . . . . 5
109rmo2 3423 . . . 4
1110imbi2i 312 . . 3
12 19.37v 1769 . . 3
1311, 12bitr4i 252 . 2
146, 8, 133bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wex 1613  wnf 1617  wral 2807  wrmo 2810 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-nf 1618  df-eu 2287  df-mo 2288  df-ral 2812  df-rmo 2815 This theorem is referenced by:  2reu1  32394
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