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Theorem imim12d 72
Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.)
Hypotheses
Ref Expression
imim12d.1 (𝜑 → (𝜓𝜒))
imim12d.2 (𝜑 → (𝜃𝜏))
Assertion
Ref Expression
imim12d (𝜑 → ((𝜒𝜃) → (𝜓𝜏)))

Proof of Theorem imim12d
StepHypRef Expression
1 imim12d.1 . 2 (𝜑 → (𝜓𝜒))
2 imim12d.2 . . 3 (𝜑 → (𝜃𝜏))
32imim2d 52 . 2 (𝜑 → ((𝜒𝜃) → (𝜒𝜏)))
41, 3syl5d 66 1 (𝜑 → ((𝜒𝜃) → (𝜓𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  imim1d  73  equveli  1658  hbsb4t  1905  mo23  1957  rspcimdv  2674  r19.29uz  9819  setindis  10479  bdsetindis  10481  bj-findis  10491
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