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  7349  f1ocnv2d  7675  oelim  8543  zorn2lem7  10581  addrid  11491  initoeu1  18187  termoeu1  18194  issubg4  19357  lmodvsdir  21162  lmodvsass  21163  gsummatr01lem4  22974  dvfsumrlim3  26354  wwlksext2clwwlk  30649  shscli  31920  f1o3d  33221  slmdvsdir  33778  slmdvsass  33779  lshpcmp  40047  relpfrlem  45944