Theorem pm4.1 143

Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116.

Assertion

Ref	Expression
pm4.1	|- ((ph -> ps) <-> (-. ps -> -. ph))

Proof of Theorem pm4.1

Step	Hyp	Ref	Expression
1		con3 86	. 2 |- ((ph -> ps) -> (-. ps -> -. ph))
2		ax-3 5	. 2 |- ((-. ps -> -. ph) -> (ph -> ps))
3	1, 2	impbi 139	1 |- ((ph -> ps) <-> (-. ps -> -. ph))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127

This theorem is referenced by:  pm4.11 400  imbi1d 465  dfom2 2374  kmlem4 3583  indstr 4611

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

This theorem depends on definitions:  df-bi 128

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