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Theorem expl 378
Description: Export a wff from a left conjunct. (Contributed by Jeff Hankins, 28-Aug-2009.)
Hypothesis
Ref Expression
expl.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
expl (𝜑 → ((𝜓𝜒) → 𝜃))

Proof of Theorem expl
StepHypRef Expression
1 expl.1 . . 3 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
21exp31 364 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32impd 254 1 (𝜑 → ((𝜓𝜒) → 𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem is referenced by:  ssenen  6845  recclnq  7382  shftfvalg  10811  shftfval  10814  fsum2dlemstep  11426  fprod2dlemstep  11614  prmpwdvds  12336  tgtop  13235
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