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Theorem nf3and 1776
Description: Deduction form of bound-variable hypothesis builder nf3an 1786. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.)
Hypotheses
Ref Expression
nfnd.1  |-  ( ph  ->  F/ x ps )
nfimd.2  |-  ( ph  ->  F/ x ch )
nfimd.3  |-  ( ph  ->  F/ x th )
Assertion
Ref Expression
nf3and  |-  ( ph  ->  F/ x ( ps 
/\  ch  /\  th )
)

Proof of Theorem nf3and
StepHypRef Expression
1 df-3an 936 . 2  |-  ( ( ps  /\  ch  /\  th )  <->  ( ( ps 
/\  ch )  /\  th ) )
2 nfnd.1 . . . 4  |-  ( ph  ->  F/ x ps )
3 nfimd.2 . . . 4  |-  ( ph  ->  F/ x ch )
42, 3nfand 1775 . . 3  |-  ( ph  ->  F/ x ( ps 
/\  ch ) )
5 nfimd.3 . . 3  |-  ( ph  ->  F/ x th )
64, 5nfand 1775 . 2  |-  ( ph  ->  F/ x ( ( ps  /\  ch )  /\  th ) )
71, 6nfxfrd 1561 1  |-  ( ph  ->  F/ x ( ps 
/\  ch  /\  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934   F/wnf 1534
This theorem is referenced by:  riotasv2dOLD  6366
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-nf 1535
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