Theorem con2 136

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 23	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜑 → ¬ 𝜓))
2	1	con2d 135	1 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  con2b  362  cesare  2702  festino  2704  calemes  2717  fesapo  2721  rexdifi  4107  elirrvOLD  9570  isprm5  16791  bj-con2com  37194  bj-axtd  37228