Theorem nfaltop 36480

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 36458	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		nfaltop.1	. . . 4 ⊢ Ⅎ𝑥𝐴
3	2	nfsn 4672	. . 3 ⊢ Ⅎ𝑥{𝐴}
4		nfaltop.2	. . . . 5 ⊢ Ⅎ𝑥𝐵
5	4	nfsn 4672	. . . 4 ⊢ Ⅎ𝑥{𝐵}
6	2, 5	nfpr 4657	. . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}}
7	3, 6	nfpr 4657	. 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}}
8	1, 7	nfcxfr 2922	1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫

This proof depends on syntax axioms:  Ⅎwnfc 2909  {csn 4588  {cpr 4590  ⟪caltop 36456

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-10 2175  ax-11 2191  ax-12 2212  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-ex 1809  df-nf 1813  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-nfc 2911  df-v 3456  df-un 3909  df-sn 4589  df-pr 4591  df-altop 36458

This theorem is used by:  sbcaltop  36481