Theorem nfaltop 36547

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 36525	. 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2		nfaltop.1	. . . 4 ⊢ Ⅎ𝑥𝐴
3	2	nfsn 4671	. . 3 ⊢ Ⅎ𝑥{𝐴}
4		nfaltop.2	. . . . 5 ⊢ Ⅎ𝑥𝐵
5	4	nfsn 4671	. . . 4 ⊢ Ⅎ𝑥{𝐵}
6	2, 5	nfpr 4656	. . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}}
7	3, 6	nfpr 4656	. 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}}
8	1, 7	nfcxfr 2922	1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫

This proof depends on syntax axioms:  Ⅎwnfc 2909  {csn 4587  {cpr 4589  ⟪caltop 36523

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-10 2178  ax-11 2194  ax-12 2215  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-nfc 2911  df-v 3455  df-un 3907  df-sn 4588  df-pr 4590  df-altop 36525

This theorem is used by:  sbcaltop  36548