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Theorem anclb 569
Description: Conjoin antecedent to left of consequent. Theorem *4.7 of [WhiteheadRussell] p. 120. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
anclb ((𝜑𝜓) ↔ (𝜑 → (𝜑𝜓)))

Proof of Theorem anclb
StepHypRef Expression
1 ibar 524 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21pm5.74i 260 1 ((𝜑𝜓) ↔ (𝜑 → (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  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:  pm4.71  663  difin  3894  bnj1021  31160  ralanid  34152  dihglblem6  36946
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