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Theorem currysetlem2 36949
Description: Lemma for currysetALT 36951. (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 36948 . . 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 1540  wcel 2108  {cab 2714
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-v 3482
This theorem is referenced by:  currysetlem3  36950
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