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Theorem nfand 1547
 Description: If in a context is not free in and , it is not free in . (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfand.1
nfand.2
Assertion
Ref Expression
nfand

Proof of Theorem nfand
StepHypRef Expression
1 nfand.1 . . . 4
2 nfand.2 . . . 4
31, 2jca 304 . . 3
4 df-nf 1437 . . . . . 6
5 df-nf 1437 . . . . . 6
64, 5anbi12i 455 . . . . 5
7 19.26 1457 . . . . 5
86, 7bitr4i 186 . . . 4
9 anim12 341 . . . . . 6
10 19.26 1457 . . . . . 6
119, 10syl6ibr 161 . . . . 5
1211alimi 1431 . . . 4
138, 12sylbi 120 . . 3
143, 13syl 14 . 2
15 df-nf 1437 . 2
1614, 15sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  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-gen 1425 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  nf3and  1548  nfbid  1567  nfsbxy  1915  nfsbxyt  1916  nfeld  2297  nfrexdxy  2468  nfreudxy  2604  nfifd  3499  nfriotadxy  5738  bdsepnft  13115
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