Theorem mpbi2and 938

Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 6-Nov-2011.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Hypotheses

Ref	Expression
mpbi2and.1	|- ( ph -> ps )
mpbi2and.2	|- ( ph -> ch )
mpbi2and.3	|- ( ph -> ( ( ps /\ ch ) <-> th ) )

Assertion

Ref	Expression
mpbi2and	|- ( ph -> th )

Proof of Theorem mpbi2and

Step	Hyp	Ref	Expression
1		mpbi2and.1	. . 3 |- ( ph -> ps )
2		mpbi2and.2	. . 3 |- ( ph -> ch )
3	1, 2	jca 304	. 2 |- ( ph -> ( ps /\ ch ) )
4		mpbi2and.3	. 2 |- ( ph -> ( ( ps /\ ch ) <-> th ) )
5	3, 4	mpbid 146	1 |- ( ph -> th )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  supisoti  6983  remim  10811  resqrtcl  10980  divalgmod  11873  oddpwdclemxy  12110  divnumden  12137  numdensq  12143  prmdivdiv  12178  4sqlem7  12323  ismgmid2  12621  mnd1  12666  topgele  12780  lmcn2  13033