Theorem con2i 630

Description: A contraposition inference. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.) (Proof shortened by Wolf Lammen, 13-Jun-2013.)

Hypothesis

Ref	Expression
con2i.a	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
con2i	⊢ (𝜓 → ¬ 𝜑)

Proof of Theorem con2i

Step	Hyp	Ref	Expression
1		con2i.a	. 2 ⊢ (𝜑 → ¬ 𝜓)
2		id 19	. 2 ⊢ (𝜓 → 𝜓)
3	1, 2	nsyl3 629	1 ⊢ (𝜓 → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 617  ax-in2 618

This theorem is referenced by:  nsyl  631  notnot  632  imanim  692  imnan  694  pm4.53r  756  ioran  757  pm3.1  759  oranim  786  xornbi  1428  exalim  1548  exnalim  1692  festino  2184  calemes  2194  fresison  2196  calemos  2197  fesapo  2198  nner  2404  necon2ai  2454  necon2bi  2455  neneqad  2479  ralexim  2522  rexalim  2523  eueq3dc  2978  elndif  3329  ssddif  3439  unssdif  3440  n0i  3498  preleq  4651  dcextest  4677  dmsn0el  5204  funtpg  5378  ftpg  5833  acexmidlemab  6007  reldmtpos  6414  nntri2  6657  nntri3  6660  nndceq  6662  inffiexmid  7093  ctssdccl  7304  mkvprop  7351  elni2  7527  renfdisj  8232  sup3exmid  9130  fzdisj  10280  sumrbdclem  11931  prodrbdclem  12125  lgsval2lem  15732  g0wlk0  16181  clwwlknnn  16221