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Theorem simplbiim 373
Description: Implication from an eliminated conjunct equivalent to the antecedent. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
simplbiim.1 (𝜑 ↔ (𝜓𝜒))
simplbiim.2 (𝜒𝜃)
Assertion
Ref Expression
simplbiim (𝜑𝜃)

Proof of Theorem simplbiim
StepHypRef Expression
1 simplbiim.1 . 2 (𝜑 ↔ (𝜓𝜒))
2 simplbiim.2 . . 3 (𝜒𝜃)
32adantl 266 . 2 ((𝜓𝜒) → 𝜃)
41, 3sylbi 118 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
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:  zltaddlt1le  8975  oddnn02np1  10192
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