Theorem expdimp 259

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

Hypothesis

Ref	Expression
exp3a.1	⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))

Assertion

Ref	Expression
expdimp	⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃))

Proof of Theorem expdimp

Step	Hyp	Ref	Expression
1		exp3a.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
2	1	expd 258	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	imp 124	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃))

Syntax hints:   → wi 4   ∧ wa 104

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 is referenced by:  rexlimdvv  2657  reu6  2995  fun11iun  5604  poxp  6397  smoel  6466  iinerm  6776  suplub2ti  7200  infglbti  7224  infnlbti  7225  prarloclemlo  7714  peano5uzti  9588  lbzbi  9850  ssfzo12bi  10471  cau3lem  11676  summodc  11946  mertenslem2  12099  prodmodclem2  12140  alzdvds  12417  nno  12469  nn0seqcvgd  12615  lcmdvds  12653  divgcdodd  12717  prmpwdvds  12930  cnptoprest  14966  lmss  14973  txlm  15006  incistruhgr  15944