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Theorem nfre1 2453
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 2399 . 2 (∃𝑥𝐴 𝜑 ↔ ∃𝑥(𝑥𝐴𝜑))
2 nfe1 1457 . 2 𝑥𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1435 1 𝑥𝑥𝐴 𝜑
Colors of variables: wff set class
Syntax hints:  wa 103  wnf 1421  wex 1453  wcel 1465  wrex 2394
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 1408  ax-gen 1410  ax-ie1 1454
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-rex 2399
This theorem is referenced by:  r19.29an  2551  nfiu1  3813  fun11iun  5356  eusvobj2  5728  fodjuomnilemdc  6984  ismkvnex  6997  prarloclem3step  7272  prmuloc2  7343  ltexprlemm  7376  caucvgprprlemaddq  7484  caucvgsrlemgt1  7571  axpre-suploclemres  7677  supinfneg  9358  infsupneg  9359  lbzbi  9376  divalglemeunn  11545  divalglemeuneg  11547  bezoutlemmain  11613  bezout  11626  isomninnlem  13152
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