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Theorem conss34 27623
 Description: Contrpositive law for subsets. (Contributed by Andrew Salmon, 15-Jul-2011.)
Assertion
Ref Expression
conss34

Proof of Theorem conss34
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 con34b 285 . . . 4
2 compel 27619 . . . . 5
3 compel 27619 . . . . 5
42, 3imbi12i 318 . . . 4
51, 4bitr4i 245 . . 3
65albii 1576 . 2
7 dfss2 3339 . 2
8 dfss2 3339 . 2
96, 7, 83bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550   wcel 1726  cvv 2958   cdif 3319   wss 3322 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336
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