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Theorem iman 413
Description: Express implication in terms of conjunction. Theorem 3.4(27) of [Stoll] p. 176. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 30-Oct-2012.)
Assertion
Ref Expression
iman

Proof of Theorem iman
StepHypRef Expression
1 notnot 282 . . 3
21imbi2i 303 . 2
3 imnan 411 . 2
42, 3bitri 240 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wa 358
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 177  df-an 360
This theorem is referenced by:  annim  414  pm3.24  852  xor  861  nannan  1291  nic-mpALT  1437  nic-axALT  1439  difdif  3392  dfss4  3489  difin  3492  npss0  3589  ssdif0  3609  difin0ss  3616  inssdif0  3617  dfif2  3664  dfimak2  4298
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