Theorem pm4.1 164

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 94	. 2 |- ((ph -> ps) -> (-. ps -> -. ph))
2		ax-3 6	. 2 |- ((-. ps -> -. ph) -> (ph -> ps))
3	1, 2	impbi 157	1 |- ((ph -> ps) <-> (-. ps -> -. ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146

This theorem is referenced by:  pm4.79 355  pm4.11 520  imbi1d 611  dfom2 3123  indstr 6393  ntreq0 7650

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

This theorem depends on definitions:  df-bi 147

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