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Theorem sbcaltop 25826
 Description: Distribution of class substitution over alternate ordered pairs. (Contributed by Scott Fenton, 25-Sep-2015.)
Assertion
Ref Expression
sbcaltop
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcaltop
StepHypRef Expression
1 nfcsb1v 3283 . . . 4
2 nfcsb1v 3283 . . . 4
31, 2nfaltop 25825 . . 3
43a1i 11 . 2
5 csbeq1a 3259 . . . 4
6 altopeq1 25808 . . . 4
75, 6syl 16 . . 3
8 csbeq1a 3259 . . . 4
9 altopeq2 25809 . . . 4
108, 9syl 16 . . 3
117, 10eqtrd 2468 . 2
124, 11csbiegf 3291 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wnfc 2559  cvv 2956  csb 3251  caltop 25801 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-sn 3820  df-pr 3821  df-altop 25803
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