Theorem exp53 375

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 114	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜏 → 𝜂))
3	2	exp43 370	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  xpdom2  6809  elfzodifsumelfzo  10157  grplcan  12761