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Theorem nfaltop 25825
Description: Bound-variable hypothesis builder for alternate ordered pairs. (Contributed by Scott Fenton, 25-Sep-2015.)
Hypotheses
Ref Expression
nfaltop.1  |-  F/_ x A
nfaltop.2  |-  F/_ x B
Assertion
Ref Expression
nfaltop  |-  F/_ x << A ,  B >>

Proof of Theorem nfaltop
StepHypRef Expression
1 df-altop 25803 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 nfaltop.1 . . . 4  |-  F/_ x A
32nfsn 3866 . . 3  |-  F/_ x { A }
4 nfaltop.2 . . . . 5  |-  F/_ x B
54nfsn 3866 . . . 4  |-  F/_ x { B }
62, 5nfpr 3855 . . 3  |-  F/_ x { A ,  { B } }
73, 6nfpr 3855 . 2  |-  F/_ x { { A } ,  { A ,  { B } } }
81, 7nfcxfr 2569 1  |-  F/_ x << A ,  B >>
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2559   {csn 3814   {cpr 3815   <<caltop 25801
This theorem is referenced by:  sbcaltop  25826
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-sn 3820  df-pr 3821  df-altop 25803
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