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Theorem nf3an 1546
Description: If  x is not free in  ph,  ps, and  ch, it is not free in  ( ph  /\  ps  /\  ch ). (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfan.1  |-  F/ x ph
nfan.2  |-  F/ x ps
nfan.3  |-  F/ x ch
Assertion
Ref Expression
nf3an  |-  F/ x
( ph  /\  ps  /\  ch )

Proof of Theorem nf3an
StepHypRef Expression
1 df-3an 965 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
2 nfan.1 . . . 4  |-  F/ x ph
3 nfan.2 . . . 4  |-  F/ x ps
42, 3nfan 1545 . . 3  |-  F/ x
( ph  /\  ps )
5 nfan.3 . . 3  |-  F/ x ch
64, 5nfan 1545 . 2  |-  F/ x
( ( ph  /\  ps )  /\  ch )
71, 6nfxfr 1451 1  |-  F/ x
( ph  /\  ps  /\  ch )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    /\ w3a 963   F/wnf 1437
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 1424  ax-gen 1426  ax-4 1488
This theorem depends on definitions:  df-bi 116  df-3an 965  df-nf 1438
This theorem is referenced by:  vtocl3gaf  2758  mob  2869  nfop  3728  mkvprop  7039  seq3f1olemstep  10304  seq3f1olemp  10305  nfsum1  11156  nfsum  11157
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