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Theorem nic-ich 1450
Description: Chained inference. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-ich.1 (φ (ψ ψ))
nic-ich.2 (ψ (χ χ))
Assertion
Ref Expression
nic-ich (φ (χ χ))

Proof of Theorem nic-ich
StepHypRef Expression
1 nic-ich.2 . . 3 (ψ (χ χ))
21nic-isw1 1445 . 2 ((χ χ) ψ)
3 nic-ich.1 . . 3 (φ (ψ ψ))
43nic-imp 1440 . 2 (((χ χ) ψ) ((φ (χ χ)) (φ (χ χ))))
52, 4nic-mp 1436 1 (φ (χ χ))
Colors of variables: wff setvar class
Syntax hints:   wnan 1287
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  df-nan 1288
This theorem is referenced by:  nic-idbl  1451  nic-luk1  1456
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