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Theorem anabsi5 521
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 119 . 2 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
32anabss5 520 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  anabsi6  522  anabsi8  524  3anidm12  1203  equsexd  1633  rspce  2668  phplem3g  6349  ltexprlemrl  6765  ltexprlemru  6767
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