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Theorem nfnan 1986
Description: If  x is not free in  ph and  ps, then it is not free in  ( ph  -/\  ps ). (Contributed by Scott Fenton, 2-Jan-2018.)
Hypotheses
Ref Expression
nfan.1  |-  F/ x ph
nfan.2  |-  F/ x ps
Assertion
Ref Expression
nfnan  |-  F/ x
( ph  -/\  ps )

Proof of Theorem nfnan
StepHypRef Expression
1 df-nan 1381 . 2  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
2 nfan.1 . . . 4  |-  F/ x ph
3 nfan.2 . . . 4  |-  F/ x ps
42, 3nfan 1985 . . 3  |-  F/ x
( ph  /\  ps )
54nfn 1957 . 2  |-  F/ x  -.  ( ph  /\  ps )
61, 5nfxfr 1693 1  |-  F/ x
( ph  -/\  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 371    -/\ wnan 1380   F/wnf 1664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-an 373  df-nan 1381  df-ex 1661  df-nf 1665
This theorem is referenced by: (None)
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