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Theorem nfnan 1825
Description: If is not free in and , then it is not free in . (Contributed by Scott Fenton, 2-Jan-2018.)
Hypotheses
Ref Expression
nfan.1  F/
nfan.2  F/
Assertion
Ref Expression
nfnan  F/

Proof of Theorem nfnan
StepHypRef Expression
1 df-nan 1288 . 2
2 nfan.1 . . . 4  F/
3 nfan.2 . . . 4  F/
42, 3nfan 1824 . . 3  F/
54nfn 1793 . 2  F/
61, 5nfxfr 1570 1  F/
Colors of variables: wff setvar class
Syntax hints:   wn 3   wa 358   wnan 1287   F/wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  nfnin  3228
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