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Theorem nford 1456
Description: If in a context is not free in and , it is not free in . (Contributed by Jim Kingdon, 29-Oct-2019.)
Hypotheses
Ref Expression
nford.1  F/
nford.2  F/
Assertion
Ref Expression
nford  F/

Proof of Theorem nford
StepHypRef Expression
1 nford.1 . . . . 5  F/
2 nford.2 . . . . 5  F/
3 df-nf 1347 . . . . . . 7  F/
4 df-nf 1347 . . . . . . 7  F/
53, 4anbi12i 433 . . . . . 6  F/  F/
65biimpi 113 . . . . 5  F/  F/
71, 2, 6syl2anc 391 . . . 4
8 19.26 1367 . . . 4
97, 8sylibr 137 . . 3
10 orc 632 . . . . . . 7
1110alimi 1341 . . . . . 6
1211imim2i 12 . . . . 5
13 olc 631 . . . . . . 7
1413alimi 1341 . . . . . 6
1514imim2i 12 . . . . 5
1612, 15jaao 638 . . . 4
1716alimi 1341 . . 3
189, 17syl 14 . 2
19 df-nf 1347 . 2  F/
2018, 19sylibr 137 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 628  wal 1240   F/wnf 1346
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-io 629  ax-5 1333  ax-gen 1335
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  nfifd  3349
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