Theorem pm4.71i 637

Description: Inference converting an implication to a biconditional with conjunction. Inference from Theorem *4.71 of [WhiteheadRussell] p. 120.

Hypothesis

Ref	Expression
pm4.71i.1	|- (ph -> ps)

Assertion

Ref	Expression
pm4.71i	|- (ph <-> (ph /\ ps))

Proof of Theorem pm4.71i

Step	Hyp	Ref	Expression
1		pm4.71i.1	. 2 |- (ph -> ps)
2		pm4.71 635	. 2 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
3	1, 2	mpbi 189	1 |- (ph <-> (ph /\ ps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  pm4.45 640  2eu5 1453  imadmrn 3414  map0e 4342  xpsnen 4435  aceq5lem2 4736  infmap2lem1 7579  dfms2 7799  pjima 10104

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-an 225

Copyright terms: Public domain