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Theorem jca3 33156
Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 14-Oct-2010.)
Hypotheses
Ref Expression
jca3.1 (𝜑 → (𝜓𝜒))
jca3.2 (𝜃𝜏)
Assertion
Ref Expression
jca3 (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))

Proof of Theorem jca3
StepHypRef Expression
1 jca3.1 . . . . 5 (𝜑 → (𝜓𝜒))
21imp 444 . . . 4 ((𝜑𝜓) → 𝜒)
32a1d 25 . . 3 ((𝜑𝜓) → (𝜃𝜒))
4 jca3.2 . . 3 (𝜃𝜏)
53, 4jca2 33154 . 2 ((𝜑𝜓) → (𝜃 → (𝜒𝜏)))
65ex 449 1 (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))
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: (None)
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