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Theorem ifpim23g 36109
 Description: Restate implication as conditional logic operator. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpim23g if-

Proof of Theorem ifpim23g
StepHypRef Expression
1 ifpidg 36105 . 2 if-
2 dfor2 412 . . . . 5
32imbi2i 313 . . . 4
4 impexp 447 . . . 4
5 ax-1 6 . . . . . 6
65adantl 467 . . . . 5
76biantrur 508 . . . 4
83, 4, 73bitr2i 276 . . 3
9 impexp 447 . . . . 5
10 imdi 364 . . . . . 6
11 imor 413 . . . . . . . 8
12 orcom 388 . . . . . . . 8
1311, 12bitri 252 . . . . . . 7
1413imbi2i 313 . . . . . 6
1510, 14bitri 252 . . . . 5
169, 15bitri 252 . . . 4
17 pm2.21 111 . . . . . 6
1817olcd 394 . . . . 5
1918biantrur 508 . . . 4
2016, 19bitri 252 . . 3
218, 20anbi12i 701 . 2
22 ancom 451 . 2
231, 21, 223bitr2i 276 1 if-
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369   wa 370  if-wif 1420 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 188  df-or 371  df-an 372  df-ifp 1421 This theorem is referenced by:  ifpim3  36110  ifpim4  36112
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