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Theorem anim12da 32566
Description: Conjoin antecedents and consequents in a deduction. (Contributed by Jeff Madsen, 16-Jun-2011.)
Hypotheses
Ref Expression
anim12da.1 ((𝜑𝜓) → 𝜃)
anim12da.2 ((𝜑𝜒) → 𝜏)
Assertion
Ref Expression
anim12da ((𝜑 ∧ (𝜓𝜒)) → (𝜃𝜏))

Proof of Theorem anim12da
StepHypRef Expression
1 anim12da.1 . 2 ((𝜑𝜓) → 𝜃)
2 anim12da.2 . 2 ((𝜑𝜒) → 𝜏)
31, 2anim12dan 877 1 ((𝜑 ∧ (𝜓𝜒)) → (𝜃𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  ghomco  32750  rngohomco  32833  rngoisocnv  32840  rngoisoco  32841  idlsubcl  32882
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