Theorem iba 284

Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Mar-1994.) (Revised by NM, 24-Mar-2013.)

Assertion

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

Proof of Theorem iba

Step	Hyp	Ref	Expression
1		pm3.21 251	. 2 |- ( ph -> ( ps -> ( ps /\ ph ) ) )
2		simpl 102	. 2 |- ( ( ps /\ ph ) -> ps )
3	1, 2	impbid1 130	1 |- ( ph -> ( ps <-> ( ps /\ ph ) ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  biantru  286  biantrud  288  ancrb  305  rbaibd  833  dedlem0a  875  fvopab6  5264  fressnfv  5350  tpostpos  5879  nnmword  6091  ltmpig  6437