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Theorem nfaltop 35981
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 35959 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4707 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4707 . . . 4 𝑥{𝐵}
62, 5nfpr 4692 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4692 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2903 1 𝑥𝐴, 𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2890  {csn 4626  {cpr 4628  caltop 35957
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-v 3482  df-un 3956  df-sn 4627  df-pr 4629  df-altop 35959
This theorem is referenced by:  sbcaltop  35982
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