Theorem con3 94

Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103.

Assertion

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

Proof of Theorem con3

Step	Hyp	Ref	Expression
1		notnot1 86	. . 3 |- (ps -> -. -. ps)
2	1	imim2i 17	. 2 |- ((ph -> ps) -> (ph -> -. -. ps))
3	2	con2d 91	1 |- ((ph -> ps) -> (-. ps -> -. ph))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  con3d 95  impt 139  con34b 164  jao 338  mtt 717  pclem6 746  meredith 931  nic-ax 969  nic-axALT 970  ax4 1008  hbnt 1038  19.22 1075  ax11indn 1405  ralf0 2413  ivthlem7 7492  hlimuniii 9384  fcluscf 11724

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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