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Theorem nf3and 2019
Description: Deduction form of bound-variable hypothesis builder nf3an 2023. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.)
Hypotheses
Ref Expression
nfand.1  |-  ( ph  ->  F/ x ps )
nfand.2  |-  ( ph  ->  F/ x ch )
nfand.3  |-  ( ph  ->  F/ x th )
Assertion
Ref Expression
nf3and  |-  ( ph  ->  F/ x ( ps 
/\  ch  /\  th )
)

Proof of Theorem nf3and
StepHypRef Expression
1 df-3an 993 . 2  |-  ( ( ps  /\  ch  /\  th )  <->  ( ( ps 
/\  ch )  /\  th ) )
2 nfand.1 . . . 4  |-  ( ph  ->  F/ x ps )
3 nfand.2 . . . 4  |-  ( ph  ->  F/ x ch )
42, 3nfand 2018 . . 3  |-  ( ph  ->  F/ x ( ps 
/\  ch ) )
5 nfand.3 . . 3  |-  ( ph  ->  F/ x th )
64, 5nfand 2018 . 2  |-  ( ph  ->  F/ x ( ( ps  /\  ch )  /\  th ) )
71, 6nfxfrd 1707 1  |-  ( ph  ->  F/ x ( ps 
/\  ch  /\  th )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 375    /\ w3a 991   F/wnf 1677
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-3an 993  df-ex 1674  df-nf 1678
This theorem is referenced by: (None)
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