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Theorem imim12d 68
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 48 . 2 (φ → ((χθ) → (χτ)))
41, 3syl5d 62 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  69  equveli  1639  hbsb4t  1886  mo23  1938  rspcimdv  2651  setindis  9417  bdsetindis  9419  bj-findis  9429
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