Theorem nfaltop 35944

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 35922	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		nfaltop.1	. . . 4 ⊢ Ⅎ𝑥𝐴
3	2	nfsn 4732	. . 3 ⊢ Ⅎ𝑥{𝐴}
4		nfaltop.2	. . . . 5 ⊢ Ⅎ𝑥𝐵
5	4	nfsn 4732	. . . 4 ⊢ Ⅎ𝑥{𝐵}
6	2, 5	nfpr 4715	. . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}}
7	3, 6	nfpr 4715	. 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}}
8	1, 7	nfcxfr 2906	1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫

Syntax hints:  Ⅎwnfc 2893  {csn 4648  {cpr 4650  ⟪caltop 35920

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2158  ax-12 2178  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-nfc 2895  df-v 3490  df-un 3981  df-sn 4649  df-pr 4651  df-altop 35922

This theorem is referenced by:  sbcaltop  35945