Theorem con3 651

Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)

Assertion

Ref	Expression
con3	|- ( ( ph -> ps ) -> ( -. ps -> -. ph ) )

Proof of Theorem con3

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	con3d 640	1 |- ( ( ph -> ps ) -> ( -. ps -> -. ph ) )

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-in1 623  ax-in2 624

This theorem is used by:  mtt  696  annimim  697  pm3.37  700  con34bdc  883  hbnt  1705  ralf0  3630  ltleletr  8407  ltnsym  8411  lealltlt1  16751  lealltlt2  16752  bj-nnsn  16761  bj-nnclavius  16765  bj-con1st  16779