Theorem rb-imdf 1515

Description: The definition of implication, in terms of ∨ and ¬. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
rb-imdf	⊢ ¬ (¬ (¬ (φ → ψ) ∨ (¬ φ ∨ ψ)) ∨ ¬ (¬ (¬ φ ∨ ψ) ∨ (φ → ψ)))

Proof of Theorem rb-imdf

Step	Hyp	Ref	Expression
1		imor 401	. 2 ⊢ ((φ → ψ) ↔ (¬ φ ∨ ψ))
2		rb-bijust 1514	. 2 ⊢ (((φ → ψ) ↔ (¬ φ ∨ ψ)) ↔ ¬ (¬ (¬ (φ → ψ) ∨ (¬ φ ∨ ψ)) ∨ ¬ (¬ (¬ φ ∨ ψ) ∨ (φ → ψ))))
3	1, 2	mpbi 199	1 ⊢ ¬ (¬ (¬ (φ → ψ) ∨ (¬ φ ∨ ψ)) ∨ ¬ (¬ (¬ φ ∨ ψ) ∨ (φ → ψ)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  re1axmp  1529  re2luk1  1530  re2luk2  1531  re2luk3  1532