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  5660  poxp  6468  suppssrst  6501  suppssrgst  6502  smoel  6571  iinerm  6881  suplub2ti  7342  infglbti  7366  infnlbti  7367  prarloclemlo  7862  peano5uzti  9759  lbzbi  10026  ssfzo12bi  10654  cau3lem  11897  summodc  12169  mertenslem2  12322  prodmodclem2  12363  alzdvds  12640  nno  12692  nn0seqcvgd  12838  lcmdvds  12876  divgcdodd  12941  prmpwdvds  13157  cnptoprest  15431  lmss  15438  txlm  15471  incistruhgr  16497