Theorem com34 83

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 82	. 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-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  com4l  84  com35  90  3an1rs  1221  rspct  2861  po2nr  4345  funssres  5301  f1ocnv2d  6131  tfrlem9  6386  nnmass  6554  nnmordi  6583  genpcdl  7605  genpcuu  7606  mulnqprl  7654  mulnqpru  7655  distrlem1prl  7668  distrlem1pru  7669  divgt0  8918  divge0  8919  uzind2  9457  facdiv  10849  dvdsabseq  12031  divgcdcoprm0  12296  lmodvsdi  13945