Theorem nfaltop 33831

Description: Bound-variable hypothesis builder for alternate ordered pairs. (Contributed by Scott Fenton, 25-Sep-2015.)

Hypotheses

Ref	Expression
nfaltop.1	⊢ Ⅎ𝑥𝐴
nfaltop.2	⊢ Ⅎ𝑥𝐵

Assertion

Ref	Expression
nfaltop	⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫

Proof of Theorem nfaltop

Step	Hyp	Ref	Expression
1		df-altop 33809	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		nfaltop.1	. . . 4 ⊢ Ⅎ𝑥𝐴
3	2	nfsn 4600	. . 3 ⊢ Ⅎ𝑥{𝐴}
4		nfaltop.2	. . . . 5 ⊢ Ⅎ𝑥𝐵
5	4	nfsn 4600	. . . 4 ⊢ Ⅎ𝑥{𝐵}
6	2, 5	nfpr 4585	. . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}}
7	3, 6	nfpr 4585	. 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}}
8	1, 7	nfcxfr 2917	1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫

Syntax hints:  Ⅎwnfc 2899  {csn 4522  {cpr 4524  ⟪caltop 33807

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2729

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-nfc 2901  df-v 3411  df-un 3863  df-sn 4523  df-pr 4525  df-altop 33809

This theorem is referenced by:  sbcaltop  33832