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Theorem cases 970
Description: Case disjunction according to the value of . (Contributed by NM, 25-Apr-2019.)
Hypotheses
Ref Expression
cases.1
cases.2
Assertion
Ref Expression
cases

Proof of Theorem cases
StepHypRef Expression
1 exmid 415 . . 3
21biantrur 506 . 2
3 andir 868 . 2
4 cases.1 . . . 4
54pm5.32i 637 . . 3
6 cases.2 . . . 4
76pm5.32i 637 . . 3
85, 7orbi12i 521 . 2
92, 3, 83bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369
This theorem is referenced by:  casesifp  1392  elimif  3975  elim2if  27422
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-or 370  df-an 371
  Copyright terms: Public domain W3C validator