Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  currysetlem2 Structured version   Visualization version   GIF version

Theorem currysetlem2 36931
Description: Lemma for currysetALT 36933. (Contributed by BJ, 23-Sep-2023.) This proof is intuitionistically valid. (Proof modification is discouraged.)
Hypothesis
Ref Expression
currysetlem2.def 𝑋 = {𝑥 ∣ (𝑥𝑥𝜑)}
Assertion
Ref Expression
currysetlem2 (𝑋𝑉 → (𝑋𝑋𝜑))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝑉(𝑥)   𝑋(𝑥)

Proof of Theorem currysetlem2
StepHypRef Expression
1 currysetlem2.def . . . 4 𝑋 = {𝑥 ∣ (𝑥𝑥𝜑)}
21currysetlem1 36930 . . 3 (𝑋𝑉 → (𝑋𝑋 ↔ (𝑋𝑋𝜑)))
32biimpd 229 . 2 (𝑋𝑉 → (𝑋𝑋 → (𝑋𝑋𝜑)))
43pm2.43d 53 1 (𝑋𝑉 → (𝑋𝑋𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  wcel 2106  {cab 2712
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-v 3480
This theorem is referenced by:  currysetlem3  36932
  Copyright terms: Public domain W3C validator