Theorem exp42 441

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp42.1	⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
exp42	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp42

Step	Hyp	Ref	Expression
1		exp42.1	. . 3 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏)
2	1	exp31 425	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	expd 421	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  isofrlem  7340  f1ocnv2d  7666  oelim  8526  zorn2lem7  10561  addrid  11471  initoeu1  18166  termoeu1  18173  issubg4  19336  lmodvsdir  21141  lmodvsass  21142  gsummatr01lem4  22953  dvfsumrlim3  26333  wwlksext2clwwlk  30630  shscli  31901  f1o3d  33202  slmdvsdir  33759  slmdvsass  33760  lshpcmp  40013  relpfrlem  45895