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Theorem anabsi8 856
Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999.)
Hypothesis
Ref Expression
anabsi8.1 (𝜓 → ((𝜓𝜑) → 𝜒))
Assertion
Ref Expression
anabsi8 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsi8
StepHypRef Expression
1 anabsi8.1 . . 3 (𝜓 → ((𝜓𝜑) → 𝜒))
21anabsi5 853 . 2 ((𝜓𝜑) → 𝜒)
32ancoms 467 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  subuhgr  40509  subupgr  40510  subumgr  40511  subusgr  40512
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