Theorem com3l 81

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 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
com3l	⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃)))

Proof of Theorem com3l

Step	Hyp	Ref	Expression
1		com3.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com3r 79	. 2 ⊢ (𝜒 → (𝜑 → (𝜓 → 𝜃)))
3	2	com3r 79	1 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  com4l  84  impd  254  3imp231  1197  expdcom  1442  nebidc  2427  sbcimdv  3028  prel12  3771  reusv3  4460  relcoi1  5160  oprabid  5906  poxp  6232  reldmtpos  6253  tfrlem9  6319  tfri3  6367  ordiso2  7033  distrlem5prl  7584  distrlem5pru  7585  bndndx  9174  uzind2  9364  leexp1a  10574  cncongr1  12102  infpnlem1  12356  bj-inf2vnlem2  14693