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Theorem impl 373
Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014.)
Hypothesis
Ref Expression
impl.1 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
impl (((𝜑𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem impl
StepHypRef Expression
1 impl.1 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
21expd 255 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32imp31 253 1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  sbc2iedv  2912  csbie2t  2977  foco2  5547  erth  6350  distrlem1prl  7195  distrlem1pru  7196  uz11  9095  divgcdcoprm0  11415  cncongr1  11417
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