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Theorem nfcriv 2964
Description: Consequence of the not-free predicate, similiar to nfcri 2968. Requires 𝑦 and 𝐴 be disjoint, but is not based on ax-13 2381. (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 2963 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2ax-mp 5 1 𝑥 𝑦𝐴
Colors of variables: wff setvar class
Syntax hints:  wnf 1775  wcel 2105  wnfc 2958
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-ex 1772  df-nfc 2960
This theorem is referenced by:  nfcrii  2967  nfnfc  2987  cleqf  3007  nfccdeq  3766  csbgfi  3900  dfss2f  3955  iunxsngf  5005  fedgmullem2  30925
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