Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nfaltop Structured version   Visualization version   GIF version

Theorem nfaltop 31257
 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 31235 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4189 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4189 . . . 4 𝑥{𝐵}
62, 5nfpr 4179 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4179 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2749 1 𝑥𝐴, 𝐵
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2738  {csn 4125  {cpr 4127  ⟪caltop 31233 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-sn 4126  df-pr 4128  df-altop 31235 This theorem is referenced by:  sbcaltop  31258
 Copyright terms: Public domain W3C validator