Theorem com14 87

Description: Commutation of antecedents. Swap 1st 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
com14	⊢ (𝜃 → (𝜓 → (𝜒 → (𝜑 → 𝜏))))

Proof of Theorem com14

Step	Hyp	Ref	Expression
1		com4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	com4l 83	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → (𝜑 → 𝜏))))
3	2	com3r 78	1 ⊢ (𝜃 → (𝜓 → (𝜒 → (𝜑 → 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:  f1o2ndf1  5869  fz0fzdiffz0  9141  elfzodifsumelfzo  9210  ssfzo12  9233  dfgcd2  10403  cncongr1  10485