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Theorem rmoimia 3036
 Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
rmoimia.1 (x A → (φψ))
Assertion
Ref Expression
rmoimia (∃*x A ψ∃*x A φ)

Proof of Theorem rmoimia
StepHypRef Expression
1 rmoim 3035 . 2 (x A (φψ) → (∃*x A ψ∃*x A φ))
2 rmoimia.1 . 2 (x A → (φψ))
31, 2mprg 2683 1 (∃*x A ψ∃*x A φ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  ∃*wrmo 2617 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 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-ral 2619  df-rmo 2622 This theorem is referenced by: (None)
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