ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  r19.29af GIF version

Theorem r19.29af 2635
Description: A commonly used pattern based on r19.29 2631. (Contributed by Thierry Arnoux, 29-Nov-2017.)
Hypotheses
Ref Expression
r19.29af.0 𝑥𝜑
r19.29af.1 (((𝜑𝑥𝐴) ∧ 𝜓) → 𝜒)
r19.29af.2 (𝜑 → ∃𝑥𝐴 𝜓)
Assertion
Ref Expression
r19.29af (𝜑𝜒)
Distinct variable group:   𝜒,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem r19.29af
StepHypRef Expression
1 r19.29af.0 . 2 𝑥𝜑
2 nfv 1539 . 2 𝑥𝜒
3 r19.29af.1 . 2 (((𝜑𝑥𝐴) ∧ 𝜓) → 𝜒)
4 r19.29af.2 . 2 (𝜑 → ∃𝑥𝐴 𝜓)
51, 2, 3, 4r19.29af2 2634 1 (𝜑𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wnf 1471  wcel 2164  wrex 2473
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-ral 2477  df-rex 2478
This theorem is referenced by:  r19.29an  2636  r19.29a  2637  suplocsrlem  7868  supinfneg  9660  infsupneg  9661  pw1nct  15493
  Copyright terms: Public domain W3C validator