Theorem exp5c 445

Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)

Hypothesis

Ref	Expression
exp5c.1	⊢ (𝜑 → ((𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂)))

Assertion

Ref	Expression
exp5c	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp5c

Step	Hyp	Ref	Expression
1		exp5c.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂)))
2	1	exp4a 432	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → (𝜏 → 𝜂))))
3	2	expd 416	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 396

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 206  df-an 397

This theorem is referenced by:  exp5l  447  fiint  9091  inf3lem2  9387  fgcl  23029  pclfinN  37914  hbtlem2  40949