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Theorem cases2 971
Description: Case disjunction according to the value of . (Contributed by BJ, 6-Apr-2019.) (Proof shortened by Wolf Lammen, 2-Jan-2020.)
Assertion
Ref Expression
cases2

Proof of Theorem cases2
StepHypRef Expression
1 pm3.4 561 . . . 4
2 pm2.24 109 . . . . 5
32adantr 465 . . . 4
41, 3jca 532 . . 3
5 pm2.21 108 . . . . 5
65adantr 465 . . . 4
7 pm3.4 561 . . . 4
86, 7jca 532 . . 3
94, 8jaoi 379 . 2
10 pm2.27 39 . . . . . 6
1110imdistani 690 . . . . 5
1211orcd 392 . . . 4
1312adantrr 716 . . 3
14 pm2.27 39 . . . . . 6
1514imdistani 690 . . . . 5
1615olcd 393 . . . 4
1716adantrl 715 . . 3
1813, 17pm2.61ian 790 . 2
199, 18impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369
This theorem is referenced by:  dfifp2  1382  ifval  3980  bj-ifim123g  37706  bj-ifidg  37707
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
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