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Theorem mpjao3dan 1202
 Description: Eliminate a 3-way disjunction in a deduction. (Contributed by Thierry Arnoux, 13-Apr-2018.)
Hypotheses
Ref Expression
mpjao3dan.1
mpjao3dan.2
mpjao3dan.3
mpjao3dan.4
Assertion
Ref Expression
mpjao3dan

Proof of Theorem mpjao3dan
StepHypRef Expression
1 mpjao3dan.1 . . 3
2 mpjao3dan.2 . . 3
31, 2jaodan 710 . 2
4 mpjao3dan.3 . 2
5 mpjao3dan.4 . . 3
6 df-3or 886 . . 3
75, 6sylib 127 . 2
83, 4, 7mpjaodan 711 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wo 629   w3o 884 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630 This theorem depends on definitions:  df-bi 110  df-3or 886 This theorem is referenced by:  wetriext  4301  nntri3  6075  nntri2or2  6076  caucvgprlemnkj  6764  caucvgprlemnbj  6765  caucvgprprlemnkj  6790  caucvgprprlemnbj  6791  caucvgsr  6886
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