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Theorem jca32 521
Description: Join three consequents. (Contributed by FL, 1-Aug-2009.)
Hypotheses
Ref Expression
jca31.1 (φψ)
jca31.2 (φχ)
jca31.3 (φθ)
Assertion
Ref Expression
jca32 (φ → (ψ (χ θ)))

Proof of Theorem jca32
StepHypRef Expression
1 jca31.1 . 2 (φψ)
2 jca31.2 . . 3 (φχ)
3 jca31.3 . . 3 (φθ)
42, 3jca 518 . 2 (φ → (χ θ))
51, 4jca 518 1 (φ → (ψ (χ θ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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 177  df-an 360
This theorem is referenced by:  syl12anc  1180  euan  2261
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