Theorem imor 234

Description: Implication in terms of disjunction. Theorem *4.6 of [WhiteheadRussell] p. 120.

Assertion

Ref	Expression
imor	|- ((ph -> ps) <-> (-. ph \/ ps))

Proof of Theorem imor

Step	Hyp	Ref	Expression
1		pm4.13 161	. . 3 |- (ph <-> -. -. ph)
2	1	imbi1i 186	. 2 |- ((ph -> ps) <-> (-. -. ph -> ps))
3		df-or 224	. 2 |- ((-. ph \/ ps) <-> (-. -. ph -> ps))
4	2, 3	bitr4 176	1 |- ((ph -> ps) <-> (-. ph \/ ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222

This theorem is referenced by:  pm4.62 235  pm2.85 581  jcab 600  19.30 1087  ax11indi 1369  iununi 2622  chrelat2 10295

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  df-or 224

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