Theorem pm2.04 82

Description: Swap antecedents. Theorem *2.04 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)

Assertion

Ref	Expression
pm2.04	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

Proof of Theorem pm2.04

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))
2	1	com23 78	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  com34  83  com45  89  bi2.04  247  equsexd  1717  sbi2v  1880  ralcom3  2633  gencbval  2774  bj-findis  13871