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Theorem anc2l 577
Description: Conjoin antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 14-Jul-2013.)
Assertion
Ref Expression
anc2l ((𝜑 → (𝜓𝜒)) → (𝜑 → (𝜓 → (𝜑𝜒))))

Proof of Theorem anc2l
StepHypRef Expression
1 pm5.42 570 . 2 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))
21biimpi 206 1 ((𝜑 → (𝜓𝜒)) → (𝜑 → (𝜓 → (𝜑𝜒))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 386
This theorem is referenced by: (None)
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