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Theorem nfre1 2533
Description: 𝑥 is not free in 𝑥𝐴𝜑. (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 2474 . 2 (∃𝑥𝐴 𝜑 ↔ ∃𝑥(𝑥𝐴𝜑))
2 nfe1 1507 . 2 𝑥𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1485 1 𝑥𝑥𝐴 𝜑
Colors of variables: wff set class
Syntax hints:  wa 104  wnf 1471  wex 1503  wcel 2160  wrex 2469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-rex 2474
This theorem is referenced by:  r19.29an  2632  nfiu1  3931  fun11iun  5501  eusvobj2  5881  fodjuomnilemdc  7171  ismkvnex  7182  prarloclem3step  7524  prmuloc2  7595  ltexprlemm  7628  caucvgprprlemaddq  7736  caucvgsrlemgt1  7823  axpre-suploclemres  7929  supinfneg  9624  infsupneg  9625  lbzbi  9645  divalglemeunn  11957  divalglemeuneg  11959  bezoutlemmain  12030  bezout  12043  lss1d  13696  pw1nct  15206  isomninnlem  15232  trirec0  15246  ismkvnnlem  15254
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