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  6298  nnmordi  6495  fundmen  6784  fiintim  6906  elfzodifsumelfzo  10157  ssfzo12  10180  dvdsmodexp  11757  infpnlem1  12311  grpinveu  12741  cnpnei  13013