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

Theorem rexlimiv 2427
 Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rexlimiv.1 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
rexlimiv (∃𝑥𝐴 𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimiv
StepHypRef Expression
1 nfv 1421 . 2 𝑥𝜓
2 rexlimiv.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2rexlimi 2426 1 (∃𝑥𝐴 𝜑𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1393  ∃wrex 2307 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-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-ral 2311  df-rex 2312 This theorem is referenced by:  rexlimiva  2428  rexlimivw  2429  rexlimivv  2438  r19.36av  2461  r19.44av  2469  r19.45av  2470  rexn0  3319  uniss2  3611  elres  4646  ssimaex  5234  tfrlem5  5930  tfrlem8  5934  ecoptocl  6193  findcard  6345  findcard2  6346  findcard2s  6347  prnmaddl  6588  0re  7027  cnegexlem2  7187  0cnALT  7201  bndndx  8180  uzn0  8488  ublbneg  8548  rexanuz2  9589  bj-inf2vnlem2  10096
 Copyright terms: Public domain W3C validator