Theorem pm3.2im 160

Description: Theorem *3.2 of [WhiteheadRussell] p. 111, expressed with primitive connectives (see pm3.2 470). (Contributed by NM, 29-Dec-1992.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Assertion

Ref	Expression
pm3.2im	⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))

Proof of Theorem pm3.2im

Step	Hyp	Ref	Expression
1		pm2.27 42	. 2 ⊢ (𝜑 → ((𝜑 → ¬ 𝜓) → ¬ 𝜓))
2	1	con2d 134	1 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  jc  161  expi  165  expt  177  bj-bijust00  34758