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Theorem simpl2im 378
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 108 . 2 ((𝜓𝜒) → 𝜒)
3 simpl2im.2 . 2 (𝜒𝜃)
41, 2, 33syl 17 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105
This theorem is referenced by:  ndvdssub  10474
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