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Theorem ich2ex 46808
Description: Two setvar variables are always interchangeable when there are two existential quantifiers. (Contributed by SN, 23-Nov-2023.)
Assertion
Ref Expression
ich2ex [𝑥𝑦]∃𝑥𝑦𝜑

Proof of Theorem ich2ex
StepHypRef Expression
1 nfe1 2140 . 2 𝑥𝑥𝑦𝜑
2 excom 2152 . . 3 (∃𝑥𝑦𝜑 ↔ ∃𝑦𝑥𝜑)
3 nfe1 2140 . . 3 𝑦𝑦𝑥𝜑
42, 3nfxfr 1848 . 2 𝑦𝑥𝑦𝜑
51, 4ichf 46790 1 [𝑥𝑦]∃𝑥𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wex 1774  [wich 46785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-11 2147  ax-12 2167
This theorem depends on definitions:  df-bi 206  df-ex 1775  df-nf 1779  df-sb 2061  df-ich 46786
This theorem is referenced by: (None)
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