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Theorem nf3and 1458
Description: Deduction form of bound-variable hypothesis builder nf3an 1455. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.)
Hypotheses
Ref Expression
nfand.1  F/
nfand.2  F/
nfand.3  F/
Assertion
Ref Expression
nf3and  F/

Proof of Theorem nf3and
StepHypRef Expression
1 df-3an 886 . 2
2 nfand.1 . . . 4  F/
3 nfand.2 . . . 4  F/
42, 3nfand 1457 . . 3  F/
5 nfand.3 . . 3  F/
64, 5nfand 1457 . 2  F/
71, 6nfxfrd 1361 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   w3a 884   F/wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335
This theorem depends on definitions:  df-bi 110  df-3an 886  df-nf 1347
This theorem is referenced by: (None)
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