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Theorem nic-bi1 1453
Description: Inference to extract one side of an implication from a definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-bi1.1 ((φ ψ) ((φ φ) (ψ ψ)))
Assertion
Ref Expression
nic-bi1 (φ (ψ ψ))

Proof of Theorem nic-bi1
StepHypRef Expression
1 nic-bi1.1 . . . 4 ((φ ψ) ((φ φ) (ψ ψ)))
2 nic-id 1443 . . . 4 (φ (φ φ))
31, 2nic-iimp1 1447 . . 3 (φ (φ ψ))
43nic-isw2 1446 . 2 (φ (ψ φ))
54nic-idel 1449 1 (φ (ψ ψ))
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-luk1  1456  nic-luk2  1457  nic-luk3  1458
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