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Theorem pm5.18 356
Description: Theorem *5.18 of [WhiteheadRussell] p. 124. This theorem says that logical equivalence is the same as negated "exclusive-or." (Contributed by NM, 28-Jun-2002.) (Proof shortened by Andrew Salmon, 20-Jun-2011.) (Proof shortened by Wolf Lammen, 15-Oct-2013.)
Assertion
Ref Expression
pm5.18

Proof of Theorem pm5.18
StepHypRef Expression
1 pm5.501 341 . . . 4
21con1bid 330 . . 3
3 pm5.501 341 . . 3
42, 3bitr2d 254 . 2
5 nbn2 345 . . . 4
65con1bid 330 . . 3
7 nbn2 345 . . 3
86, 7bitr2d 254 . 2
94, 8pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184
This theorem is referenced by:  xor3  357  pm5.19  360  pm5.16  890  dfbi3  893  xorass  1367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185
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