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Theorem rmoimi2 3037
 Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
rmoimi2.1 x((x A φ) → (x B ψ))
Assertion
Ref Expression
rmoimi2 (∃*x B ψ∃*x A φ)

Proof of Theorem rmoimi2
StepHypRef Expression
1 rmoimi2.1 . . 3 x((x A φ) → (x B ψ))
2 moim 2250 . . 3 (x((x A φ) → (x B ψ)) → (∃*x(x B ψ) → ∃*x(x A φ)))
31, 2ax-mp 8 . 2 (∃*x(x B ψ) → ∃*x(x A φ))
4 df-rmo 2622 . 2 (∃*x B ψ∃*x(x B ψ))
5 df-rmo 2622 . 2 (∃*x A φ∃*x(x A φ))
63, 4, 53imtr4i 257 1 (∃*x B ψ∃*x A φ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540   ∈ wcel 1710  ∃*wmo 2205  ∃*wrmo 2617 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-rmo 2622 This theorem is referenced by: (None)
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