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Theorem exp5c 643
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5c.1 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
Assertion
Ref Expression
exp5c (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5c
StepHypRef Expression
1 exp5c.1 . . 3 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
21exp4a 632 . 2 (𝜑 → ((𝜓𝜒) → (𝜃 → (𝜏𝜂))))
32expd 451 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 197  df-an 385
This theorem is referenced by:  exp5l  645  fiint  8278  inf3lem2  8564  fgcl  21729  pclfinN  35504  hbtlem2  38011
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