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Theorem nfaltop 34611
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 34589 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4669 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4669 . . . 4 𝑥{𝐵}
62, 5nfpr 4652 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4652 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2902 1 𝑥𝐴, 𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2884  {csn 4587  {cpr 4589  caltop 34587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-v 3446  df-un 3916  df-sn 4588  df-pr 4590  df-altop 34589
This theorem is referenced by:  sbcaltop  34612
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