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Theorem nfaltop 24586
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 24564 . 2  |-  << A ,  B >>  =  { { A } ,  { A ,  { B } } }
2 nfaltop.1 . . . 4  |-  F/_ x A
32nfsn 3704 . . 3  |-  F/_ x { A }
4 nfaltop.2 . . . . 5  |-  F/_ x B
54nfsn 3704 . . . 4  |-  F/_ x { B }
62, 5nfpr 3693 . . 3  |-  F/_ x { A ,  { B } }
73, 6nfpr 3693 . 2  |-  F/_ x { { A } ,  { A ,  { B } } }
81, 7nfcxfr 2429 1  |-  F/_ x << A ,  B >>
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2419   {csn 3653   {cpr 3654   <<caltop 24562
This theorem is referenced by:  sbcaltop  24587
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660  df-altop 24564
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