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Theorem casesifp 1404
 Description: Version of cases 973 expressed using if-. Case disjunction according to the value of . One can see this as a proof that the two hypotheses characterize the conditional operator for propositions. For the converses, see ifptru 1399 and ifpfal 1401. (Contributed by BJ, 20-Sep-2019.)
Hypotheses
Ref Expression
casesifp.1
casesifp.2
Assertion
Ref Expression
casesifp if-

Proof of Theorem casesifp
StepHypRef Expression
1 casesifp.1 . . 3
2 casesifp.2 . . 3
31, 2cases 973 . 2
4 df-ifp 1389 . 2 if-
53, 4bitr4i 254 1 if-
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 186   wo 368   wa 369  if-wif 1388 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 187  df-or 370  df-an 371  df-ifp 1389 This theorem is referenced by:  cadifp  1489
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