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Theorem jca2r 34661
Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010.)
Hypotheses
Ref Expression
jca2r.1 (𝜑 → (𝜓𝜒))
jca2r.2 (𝜓𝜃)
Assertion
Ref Expression
jca2r (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem jca2r
StepHypRef Expression
1 jca2r.2 . . 3 (𝜓𝜃)
21a1i 11 . 2 (𝜑 → (𝜓𝜃))
3 jca2r.1 . 2 (𝜑 → (𝜓𝜒))
42, 3jcad 556 1 (𝜑 → (𝜓 → (𝜃𝜒)))
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 197  df-an 385
This theorem is referenced by:  prter2  34688
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