Theorem nfaltop 32087

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

Step	Hyp	Ref	Expression
1		df-altop 32065	. 2 |- << A , B >> = { { A } , { A , { B } } }
2		nfaltop.1	. . . 4 |- F/_ x A
3	2	nfsn 4242	. . 3 |- F/_ x { A }
4		nfaltop.2	. . . . 5 |- F/_ x B
5	4	nfsn 4242	. . . 4 |- F/_ x { B }
6	2, 5	nfpr 4232	. . 3 |- F/_ x { A , { B } }
7	3, 6	nfpr 4232	. 2 |- F/_ x { { A } , { A , { B } } }
8	1, 7	nfcxfr 2762	1 |- F/_ x << A , B >>

Syntax hints:   F/_wnfc 2751   {csn 4177   {cpr 4179   <<caltop 32063

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180  df-altop 32065

This theorem is referenced by:  sbcaltop  32088