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Theorem simplbiim 382
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 273 . 2 ((𝜓𝜒) → 𝜃)
41, 3sylbi 120 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mpodifsnif  5830  ixpm  6590  finct  6967  apsscn  8371  zltaddlt1le  9729  oddnn02np1  11473
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