Theorem impexp 263

Description: Import-export theorem. Part of Theorem *4.87 of [WhiteheadRussell] p. 122. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

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

Proof of Theorem impexp

Step	Hyp	Ref	Expression
1		pm3.3 261	. 2 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )
2		pm3.31 262	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph /\ ps ) -> ch ) )
3	1, 2	impbii 126	1 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ph -> ( ps -> ch ) ) )

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:  imp4a  349  exp4a  366  imdistan  448  pm5.3  479  pm4.87  563  nan  703  pm4.14dc  902  pm5.6dc  938  2sb6  2044  2sb6rf  2050  2exsb  2069  mor  2129  eu2  2131  moanim  2161  r2alf  2567  r3al  2594  r19.23t  2658  ceqsralt  2849  rspc2gv  2942  ralrab  2987  ralrab2  2991  euind  3013  reu2  3014  reu3  3016  rmo4  3019  rmo3f  3023  reuind  3031  rmo2ilem  3142  rmo3  3144  ralss  3314  rabss  3325  raldifb  3369  unissb  3960  elintrab  3977  ssintrab  3988  dftr5  4227  repizf2lem  4293  reusv3  4601  tfi  4724  raliunxp  4916  fununi  5444  dff13  5964  dfsmo2  6548  tfr1onlemaccex  6609  tfrcllemaccex  6622  qliftfun  6881  nnnninfeq2  7459  prime  9724  raluz  9957  raluz2  9958  ralrp  10055  facwordi  11156  modfsummod  12203  nnwosdc  12794  isprm2  12873  isprm4  12875  metcnp  15536  limcdifap  15686  bdcriota  16823  nnnninfex  16970