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Theorem nfaltop 31726
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 31704 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4213 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4213 . . . 4 𝑥{𝐵}
62, 5nfpr 4203 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4203 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2759 1 𝑥𝐴, 𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2748  {csn 4148  {cpr 4150  caltop 31702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-un 3560  df-sn 4149  df-pr 4151  df-altop 31704
This theorem is referenced by:  sbcaltop  31727
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