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Theorem nabi1i 33639
Description: Constructor rule for . (Contributed by Anthony Hart, 2-Sep-2011.)
Hypotheses
Ref Expression
nabi1i.1 (𝜑𝜓)
nabi1i.2 (𝜓𝜒)
Assertion
Ref Expression
nabi1i (𝜑𝜒)

Proof of Theorem nabi1i
StepHypRef Expression
1 nabi1i.2 . 2 (𝜓𝜒)
2 nabi1i.1 . . . 4 (𝜑𝜓)
32bicomi 225 . . 3 (𝜓𝜑)
43nanbi1i 1488 . 2 ((𝜓𝜒) ↔ (𝜑𝜒))
51, 4mpbi 231 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wb 207  wnan 1475
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 208  df-an 397  df-nan 1476
This theorem is referenced by:  nabi12i  33641
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