Theorem con2 135

Description: Contraposition. Theorem *2.03 of [WhiteheadRussell] p. 100. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)

Assertion

Ref	Expression
con2	⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))

Proof of Theorem con2

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜑 → ¬ 𝜓))
2	1	con2d 134	1 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))

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:  con2b  360  cesare  2673  festino  2675  calemes  2688  fesapo  2692  rexdifi  4080  isprm5  16412  bj-con2com  34741  bj-axtd  34776