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Theorem nfald 1733
 Description: If is not free in , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 6-Jan-2018.)
Hypotheses
Ref Expression
nfald.1
nfald.2
Assertion
Ref Expression
nfald

Proof of Theorem nfald
StepHypRef Expression
1 nfald.1 . . . 4
21nfri 1499 . . 3
3 nfald.2 . . 3
42, 3alrimih 1445 . 2
5 nfnf1 1523 . . . 4
65nfal 1555 . . 3
7 hba1 1520 . . . 4
8 sp 1488 . . . . 5
98nfrd 1500 . . . 4
107, 9hbald 1467 . . 3
116, 10nfd 1503 . 2
124, 11syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329  wnf 1436 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 1423  ax-7 1424  ax-gen 1425  ax-4 1487  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  dvelimALT  1985  dvelimfv  1986  nfeudv  2014  nfeqd  2296  nfraldxy  2467  nfiotadw  5091  nfixpxy  6611  bdsepnft  13190  strcollnft  13287
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