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Theorem rmoimia 2891
 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 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
rmoimia (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)

Proof of Theorem rmoimia
StepHypRef Expression
1 rmoim 2890 . 2 (∀𝑥𝐴 (𝜑𝜓) → (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑))
2 rmoimia.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2mprg 2493 1 (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1481  ∃*wrmo 2420 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-ral 2422  df-rmo 2425 This theorem is referenced by: (None)
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