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Theorem anclb 312
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 295 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21pm5.74i 178 1 ((𝜑𝜓) ↔ (𝜑 → (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
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:  pm4.71  381  mo3h  1996
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