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  9758  lbzbi  10025  ssfzo12bi  10653  cau3lem  11895  summodc  12166  mertenslem2  12319  prodmodclem2  12360  alzdvds  12637  nno  12689  nn0seqcvgd  12835  lcmdvds  12873  divgcdodd  12938  prmpwdvds  13154  cnptoprest  15389  lmss  15396  txlm  15429  incistruhgr  16429