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Theorem nic-bi2 1454
 Description: Inference to extract the other side of an implication from a 'biconditional' definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-bi2.1 ((φ ψ) ((φ φ) (ψ ψ)))
Assertion
Ref Expression
nic-bi2 (ψ (φ φ))

Proof of Theorem nic-bi2
StepHypRef Expression
1 nic-bi2.1 . . . 4 ((φ ψ) ((φ φ) (ψ ψ)))
21nic-isw2 1446 . . 3 ((φ ψ) ((ψ ψ) (φ φ)))
3 nic-id 1443 . . 3 (ψ (ψ ψ))
42, 3nic-iimp1 1447 . 2 (ψ (φ ψ))
54nic-idel 1449 1 (ψ (φ φ))
 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-stdmp  1455  nic-luk1  1456  nic-luk2  1457  nic-luk3  1458
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