Theorem expdimp 259

Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008.)

Hypothesis

Ref	Expression
exp3a.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Assertion

Ref	Expression
expdimp	|- ( ( ph /\ ps ) -> ( ch -> th ) )

Proof of Theorem expdimp

Step	Hyp	Ref	Expression
1		exp3a.1	. . 3 |- ( ph -> ( ( ps /\ ch ) -> th ) )
2	1	expd 258	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	imp 124	1 |- ( ( ph /\ ps ) -> ( ch -> th ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  rexlimdvv  2675  reu6  3015  ifeqeqxdc  3687  fun11iun  5663  poxp  6472  suppssrst  6505  suppssrgst  6506  smoel  6575  iinerm  6885  suplub2ti  7347  infglbti  7371  infnlbti  7372  prarloclemlo  7867  peano5uzti  9765  lbzbi  10032  ssfzo12bi  10660  cau3lem  11903  summodc  12175  mertenslem2  12328  prodmodclem2  12369  alzdvds  12646  nno  12698  nn0seqcvgd  12844  lcmdvds  12882  divgcdodd  12947  prmpwdvds  13163  cnptoprest  15465  lmss  15472  txlm  15505  incistruhgr  16536