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Theorem nfaltop 35962
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 35940 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4712 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4712 . . . 4 𝑥{𝐵}
62, 5nfpr 4697 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4697 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2901 1 𝑥𝐴, 𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2888  {csn 4631  {cpr 4633  caltop 35938
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-v 3480  df-un 3968  df-sn 4632  df-pr 4634  df-altop 35940
This theorem is referenced by:  sbcaltop  35963
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