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Theorem com3l 79
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)
Hypothesis
Ref Expression
com3.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
com3l (𝜓 → (𝜒 → (𝜑𝜃)))

Proof of Theorem com3l
StepHypRef Expression
1 com3.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
21com3r 77 . 2 (𝜒 → (𝜑 → (𝜓𝜃)))
32com3r 77 1 (𝜓 → (𝜒 → (𝜑𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  com4l  82  impd  246  expdcom  1347  nebidc  2300  sbcimdv  2851  prel12  3570  reusv3  4220  relcoi1  4877  oprabid  5565  poxp  5881  reldmtpos  5899  tfrlem9  5966  tfri3  5984  ordiso2  6415  distrlem5prl  6742  distrlem5pru  6743  bndndx  8238  uzind2  8409  leexp1a  9475  bj-inf2vnlem2  10483
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