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Theorem simpl2im 656
Description: Implication from an eliminated conjunct implied by the antecedent. (Contributed by BJ/AV, 5-Apr-2021.)
Hypotheses
Ref Expression
simpl2im.1 (𝜑 → (𝜓𝜒))
simpl2im.2 (𝜒𝜃)
Assertion
Ref Expression
simpl2im (𝜑𝜃)

Proof of Theorem simpl2im
StepHypRef Expression
1 simpl2im.1 . 2 (𝜑 → (𝜓𝜒))
2 simpr 476 . 2 ((𝜓𝜒) → 𝜒)
3 simpl2im.2 . 2 (𝜒𝜃)
41, 2, 33syl 18 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 196  df-an 385
This theorem is referenced by:  dvdsaddre2b  14867  nbgrcl  40559  usgr2trlncrct  41009  wwlksnextproplem3  41117  erclwwlksnsym  41254  erclwwlksntr  41255  av-numclwlk2lem2f  41533
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