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Theorem nfaltop 32554
Description: Bound-variable hypothesis builder for alternate ordered pairs. (Contributed by Scott Fenton, 25-Sep-2015.)
Hypotheses
Ref Expression
nfaltop.1 𝑥𝐴
nfaltop.2 𝑥𝐵
Assertion
Ref Expression
nfaltop 𝑥𝐴, 𝐵

Proof of Theorem nfaltop
StepHypRef Expression
1 df-altop 32532 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4400 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4400 . . . 4 𝑥{𝐵}
62, 5nfpr 4390 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4390 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2905 1 𝑥𝐴, 𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2894  {csn 4336  {cpr 4338  caltop 32530
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2352  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-un 3739  df-sn 4337  df-pr 4339  df-altop 32532
This theorem is referenced by:  sbcaltop  32555
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