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Theorem pm2.61da3ne 2723
 Description: Deduction eliminating three inequalities in an antecedent. (Contributed by NM, 15-Jun-2013.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypotheses
Ref Expression
pm2.61da3ne.1
pm2.61da3ne.2
pm2.61da3ne.3
pm2.61da3ne.4
Assertion
Ref Expression
pm2.61da3ne

Proof of Theorem pm2.61da3ne
StepHypRef Expression
1 pm2.61da3ne.2 . 2
2 pm2.61da3ne.3 . 2
3 pm2.61da3ne.1 . . . . 5
43a1d 25 . . . 4
5 pm2.61da3ne.4 . . . . . 6
653exp2 1215 . . . . 5
76imp4b 588 . . . 4
84, 7pm2.61dane 2721 . . 3
98imp 427 . 2
101, 2, 9pm2.61da2ne 2722 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 367   w3a 974   wceq 1405   wne 2598 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-an 369  df-3an 976  df-ne 2600 This theorem is referenced by:  trljco  33740  dvh4dimN  34448
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