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Theorem nf3and 1477
Description: Deduction form of bound-variable hypothesis builder nf3an 1474. (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 898 . 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 1476 . . 3  |-  ( ph  ->  F/ x ( ps 
/\  ch ) )
5 nfand.3 . . 3  |-  ( ph  ->  F/ x th )
64, 5nfand 1476 . 2  |-  ( ph  ->  F/ x ( ( ps  /\  ch )  /\  th ) )
71, 6nfxfrd 1380 1  |-  ( ph  ->  F/ x ( ps 
/\  ch  /\  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    /\ w3a 896   F/wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-3an 898  df-nf 1366
This theorem is referenced by: (None)
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