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Theorem nbdi 486
Description: Negated biconditional (distributive form)
Assertion
Ref Expression
nbdi (a == b)' = (((a v b) ^ a') v ((a v b) ^ b'))
Proof of Theorem nbdi
StepHypRef Expression
1 dfnb 95 . 2 (a == b)' = ((a v b) ^ (a' v b'))
2 comorr 184 . . . . 5 a C (a v b)
32comcom 453 . . . 4 (a v b) C a
43comcom2 183 . . 3 (a v b) C a'
5 comorr 184 . . . . . 6 b C (b v a)
6 ax-a2 31 . . . . . 6 (b v a) = (a v b)
75, 6cbtr 182 . . . . 5 b C (a v b)
87comcom 453 . . . 4 (a v b) C b
98comcom2 183 . . 3 (a v b) C b'
104, 9fh1 469 . 2 ((a v b) ^ (a' v b')) = (((a v b) ^ a') v ((a v b) ^ b'))
111, 10ax-r2 36 1 (a == b)' = (((a v b) ^ a') v ((a v b) ^ b'))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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