Theorem iba 300

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		pm3.21 264	. 2 |- ( ph -> ( ps -> ( ps /\ ph ) ) )
2		simpl 109	. 2 |- ( ( ps /\ ph ) -> ps )
3	1, 2	impbid1 142	1 |- ( ph -> ( ps <-> ( ps /\ ph ) ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  biantru  302  biantrud  304  ancrb  322  rbaibd  924  dedlem0a  968  fvopab6  5614  fressnfv  5705  tpostpos  6267  nnmword  6521  unfiexmid  6919  ltmpig  7340  mul0eqap  8629  sup3exmid  8916  xrmaxiflemcom  11259