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Theorem nfre1 2479
 Description: 𝑥 is not free in ∃𝑥 ∈ 𝐴𝜑. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfre1 𝑥𝑥𝐴 𝜑

Proof of Theorem nfre1
StepHypRef Expression
1 df-rex 2423 . 2 (∃𝑥𝐴 𝜑 ↔ ∃𝑥(𝑥𝐴𝜑))
2 nfe1 1473 . 2 𝑥𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1451 1 𝑥𝑥𝐴 𝜑
 Colors of variables: wff set class Syntax hints:   ∧ wa 103  Ⅎwnf 1437  ∃wex 1469   ∈ wcel 1481  ∃wrex 2418 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-rex 2423 This theorem is referenced by:  r19.29an  2577  nfiu1  3850  fun11iun  5395  eusvobj2  5767  fodjuomnilemdc  7023  ismkvnex  7036  prarloclem3step  7327  prmuloc2  7398  ltexprlemm  7431  caucvgprprlemaddq  7539  caucvgsrlemgt1  7626  axpre-suploclemres  7732  supinfneg  9416  infsupneg  9417  lbzbi  9434  divalglemeunn  11652  divalglemeuneg  11654  bezoutlemmain  11720  bezout  11733  pw1nct  13369  isomninnlem  13398  trirec0  13410  ismkvnnlem  13417
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