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Theorem conb 122
 Description: Contraposition law.
Assertion
Ref Expression
conb (ab) = (ab )

Proof of Theorem conb
StepHypRef Expression
1 ax-a2 31 . . 3 ((ab) ∪ (ab )) = ((ab ) ∪ (ab))
2 ax-a1 30 . . . . 5 a = a
3 ax-a1 30 . . . . 5 b = b
42, 32an 79 . . . 4 (ab) = (a b )
54lor 70 . . 3 ((ab ) ∪ (ab)) = ((ab ) ∪ (a b ))
61, 5ax-r2 36 . 2 ((ab) ∪ (ab )) = ((ab ) ∪ (a b ))
7 dfb 94 . 2 (ab) = ((ab) ∪ (ab ))
8 dfb 94 . 2 (ab ) = ((ab ) ∪ (a b ))
96, 7, 83tr1 63 1 (ab) = (ab )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-b 39  df-a 40 This theorem is referenced by:  di  126  wr4  199  wcon  202  wcon1  207  wcon2  208  wwfh3  218  wwfh4  219  ka4lem  229  ska3  232  nomcon5  306  nom55  336  wom2  434  u3lemax4  796  comanbn  873
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