Theorem nfaltop 32424

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 32402	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		nfaltop.1	. . . 4 ⊢ Ⅎ𝑥𝐴
3	2	nfsn 4379	. . 3 ⊢ Ⅎ𝑥{𝐴}
4		nfaltop.2	. . . . 5 ⊢ Ⅎ𝑥𝐵
5	4	nfsn 4379	. . . 4 ⊢ Ⅎ𝑥{𝐵}
6	2, 5	nfpr 4369	. . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}}
7	3, 6	nfpr 4369	. 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}}
8	1, 7	nfcxfr 2911	1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫

Syntax hints:  Ⅎwnfc 2900  {csn 4316  {cpr 4318  ⟪caltop 32400

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751

This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-un 3728  df-sn 4317  df-pr 4319  df-altop 32402

This theorem is referenced by:  sbcaltop  32425