Theorem pm3.2im 137

Description: Theorem *3.2 of [WhiteheadRussell] p. 111, expressed with primitive connectives. (Contributed by NM, 5-Aug-1993.) (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 35	. 2 ⊢ (φ → ((φ → ¬ ψ) → ¬ ψ))
2	1	con2d 107	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  139  expi  141  expt  148