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Theorem nfcriv 2939
 Description: Consequence of the not-free predicate, similiar to nfcri 2943. Requires 𝑦 and 𝐴 be disjoint, but is not based on ax-13 2344. (Contributed by Wolf Lammen, 13-May-2023.)
Hypothesis
Ref Expression
nfcriv.1 𝑥𝐴
Assertion
Ref Expression
nfcriv 𝑥 𝑦𝐴
Distinct variable groups:   𝑥,𝑦   𝑦,𝐴
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfcriv
StepHypRef Expression
1 nfcriv.1 . 2 𝑥𝐴
2 nfcr 2938 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2ax-mp 5 1 𝑥 𝑦𝐴
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1765   ∈ wcel 2081  Ⅎwnfc 2933 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-12 2141 This theorem depends on definitions:  df-bi 208  df-ex 1762  df-nfc 2935 This theorem is referenced by:  nfcrii  2942  nfnfc  2959  cleqf  2978  nfccdeq  3703  csbgfi  3829  dfss2f  3880  iunxsngf  4913  fedgmullem2  30630
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