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Theorem anabsi5 544
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 122 . 2 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
32anabss5 543 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
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:  anabsi6  545  anabsi8  547  3anidm12  1229  equsexd  1661  rspce  2710  phplem3g  6526  ltexprlemrl  7116  ltexprlemru  7118  dvdssq  10926
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