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))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  com25  91  tfrlem9  6590  nnmordi  6789  fundmen  7094  fiintim  7238  elfzodifsumelfzo  10629  ssfzo12  10652  swrdswrdlem  11490  swrdswrd  11491  wrd2ind  11509  swrdccatin1  11511  dvdsmodexp  12578  dvdsaddre2b  12624  infpnlem1  13158  grpinveu  13892  mulgass2  14412  lss1d  14769  cnpnei  15369  clwwlkccatlem  16739