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Theorem nfre1 2359
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 xx A φ

Proof of Theorem nfre1
StepHypRef Expression
1 df-rex 2306 . 2 (x A φx(x A φ))
2 nfe1 1382 . 2 xx(x A φ)
31, 2nfxfr 1360 1 xx A φ
Colors of variables: wff set class
Syntax hints:   wa 97  wnf 1346  wex 1378   wcel 1390  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-rex 2306
This theorem is referenced by:  nfiu1  3678  fun11iun  5090  eusvobj2  5441  prarloclem3step  6479  prmuloc2  6548  ltexprlemm  6574  lbzbi  8327
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