Theorem com34 82

Description: Commutation of antecedents. Swap 3rd and 4th. (Contributed by NM, 25-Apr-1994.)

Hypothesis

Ref	Expression
com4.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Assertion

Ref	Expression
com34	⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏))))

Proof of Theorem com34

Step	Hyp	Ref	Expression
1		com4.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2		pm2.04 81	. 2 ⊢ ((𝜒 → (𝜃 → 𝜏)) → (𝜃 → (𝜒 → 𝜏)))
3	1, 2	syl6 33	1 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏))))

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  83  com35  89  3an1rs  1153  rspct  2708  po2nr  4109  funssres  5018  f1ocnv2d  5799  tfrlem9  6032  nnmass  6196  nnmordi  6221  genpcdl  7015  genpcuu  7016  mulnqprl  7064  mulnqpru  7065  distrlem1prl  7078  distrlem1pru  7079  divgt0  8261  divge0  8262  uzind2  8784  facdiv  10035  dvdsabseq  10715  divgcdcoprm0  10950