Theorem exp53 447

Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.)

Hypothesis

Ref	Expression
exp53.1	⊢ ((((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
exp53	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp53

Step	Hyp	Ref	Expression
1		exp53.1	. . 3 ⊢ ((((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂)
2	1	ex 412	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜏 → 𝜂))
3	2	exp43 436	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

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:  omordi  8586  xpdom2  9089  elfzodifsumelfzo  13752  grplcan  18987  2clwwlk2clwwlk  30297  grpolcan  30477