Theorem com24 87

Description: Commutation of antecedents. Swap 2nd and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

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

Assertion

Ref	Expression
com24	⊢ (𝜑 → (𝜃 → (𝜒 → (𝜓 → 𝜏))))

Proof of Theorem com24

Step	Hyp	Ref	Expression
1		com4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	com4t 85	. 2 ⊢ (𝜒 → (𝜃 → (𝜑 → (𝜓 → 𝜏))))
3	2	com13 80	1 ⊢ (𝜑 → (𝜃 → (𝜒 → (𝜓 → 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:  com25  91  tfrlem9  6471  nnmordi  6670  fundmen  6967  fiintim  7104  elfzodifsumelfzo  10419  ssfzo12  10442  swrdswrdlem  11251  swrdswrd  11252  wrd2ind  11270  swrdccatin1  11272  dvdsmodexp  12321  dvdsaddre2b  12367  infpnlem1  12897  grpinveu  13586  mulgass2  14036  lss1d  14362  cnpnei  14908  clwwlkccatlem  16137