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Theorem pm5.32 636
Description: Distribution of implication over biconditional. Theorem *5.32 of [WhiteheadRussell] p. 125. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
pm5.32

Proof of Theorem pm5.32
StepHypRef Expression
1 notbi 295 . . . 4
21imbi2i 312 . . 3
3 pm5.74 244 . . 3
4 notbi 295 . . 3
52, 3, 43bitri 271 . 2
6 df-an 371 . . 3
7 df-an 371 . . 3
86, 7bibi12i 315 . 2
95, 8bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369
This theorem is referenced by:  pm5.32i  637  pm5.32d  639  xordi  895  cbvex2OLD  2029  rabbi  3036  rabxfrd  4673  asymref  5388  mpt22eqb  6411  cfilucfil4OLD  21759  cfilucfil4  21760  wl-ax11-lem8  30032  2sb5nd  33333  2sb5ndVD  33710  2sb5ndALT  33732
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  df-an 371
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