ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rmoimia GIF version

Theorem rmoimia 2735
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 2734 . 2 (x A (φψ) → (∃*x A ψ∃*x A φ))
2 rmoimia.1 . 2 (x A → (φψ))
31, 2mprg 2372 1 (∃*x A ψ∃*x A φ)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  ∃*wrmo 2303
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-ral 2305  df-rmo 2308
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator