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  7341  infglbti  7365  infnlbti  7366  prarloclemlo  7861  peano5uzti  9754  lbzbi  10016  ssfzo12bi  10643  cau3lem  11880  summodc  12150  mertenslem2  12303  prodmodclem2  12344  alzdvds  12621  nno  12673  nn0seqcvgd  12819  lcmdvds  12857  divgcdodd  12921  prmpwdvds  13134  cnptoprest  15340  lmss  15347  txlm  15380  incistruhgr  16331