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Theorem pm5.18 347
 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 pm5.501 332 . . . 4
21con1bid 322 . . 3
3 pm5.501 332 . . 3
42, 3bitr2d 247 . 2
5 nbn2 336 . . . 4
65con1bid 322 . . 3
7 nbn2 336 . . 3
86, 7bitr2d 247 . 2
94, 8pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 5   wb 178 This theorem is referenced by:  xor3  348  pm5.19  351  pm5.16  865  dfbi3  868  xorass  1304 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10 This theorem depends on definitions:  df-bi 179
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