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Theorem rb-bijust 1514
 Description: Justification for rb-imdf 1515. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-bijust ((φψ) ↔ ¬ (¬ (¬ φ ψ) ¬ (¬ ψ φ)))

Proof of Theorem rb-bijust
StepHypRef Expression
1 dfbi1 184 . 2 ((φψ) ↔ ¬ ((φψ) → ¬ (ψφ)))
2 imor 401 . . . 4 ((φψ) ↔ (¬ φ ψ))
3 imor 401 . . . . 5 ((ψφ) ↔ (¬ ψ φ))
43notbii 287 . . . 4 (¬ (ψφ) ↔ ¬ (¬ ψ φ))
52, 4imbi12i 316 . . 3 (((φψ) → ¬ (ψφ)) ↔ ((¬ φ ψ) → ¬ (¬ ψ φ)))
65notbii 287 . 2 (¬ ((φψ) → ¬ (ψφ)) ↔ ¬ ((¬ φ ψ) → ¬ (¬ ψ φ)))
7 pm4.62 408 . . 3 (((¬ φ ψ) → ¬ (¬ ψ φ)) ↔ (¬ (¬ φ ψ) ¬ (¬ ψ φ)))
87notbii 287 . 2 (¬ ((¬ φ ψ) → ¬ (¬ ψ φ)) ↔ ¬ (¬ (¬ φ ψ) ¬ (¬ ψ φ)))
91, 6, 83bitri 262 1 ((φψ) ↔ ¬ (¬ (¬ φ ψ) ¬ (¬ ψ φ)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-or 359 This theorem is referenced by:  rb-imdf  1515
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