Theorem exp42 435

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 419	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	expd 415	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by:  isofrlem  7318  f1ocnv2d  7645  oelim  8501  zorn2lem7  10462  addrid  11361  initoeu1  17980  termoeu1  17987  issubg4  19084  lmodvsdir  20799  lmodvsass  20800  gsummatr01lem4  22552  dvfsumrlim3  25947  wwlksext2clwwlk  29993  shscli  31253  f1o3d  32558  slmdvsdir  33176  slmdvsass  33177  lshpcmp  38988  relpfrlem  44950