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Theorem imp4a 341
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
imp4a (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))

Proof of Theorem imp4a
StepHypRef Expression
1 imp4.1 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
2 impexp 259 . 2 (((𝜒𝜃) → 𝜏) ↔ (𝜒 → (𝜃𝜏)))
31, 2syl6ibr 160 1 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  imp4b  342  imp4d  344  imp55  353  imp511  354  equs5or  1758  reuss2  3279  tfrlem9  6084  facwordi  10144  ndvdssub  11204
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