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Theorem anabsi5 513
Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsi5.1 (𝜑 → ((𝜑𝜓) → 𝜒))
Assertion
Ref Expression
anabsi5 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsi5
StepHypRef Expression
1 anabsi5.1 . . 3 (𝜑 → ((𝜑𝜓) → 𝜒))
21imp 115 . 2 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
32anabss5 512 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  anabsi6  514  anabsi8  516  3anidm12  1192  equsexd  1617  rspce  2648  phplem3g  6306  ltexprlemrl  6689  ltexprlemru  6691
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