Theorem rb-ax4 1520

Description: The fourth of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
rb-ax4	⊢ (¬ (φ ∨ φ) ∨ φ)

Proof of Theorem rb-ax4

Step	Hyp	Ref	Expression
1		pm1.2 499	. . . 4 ⊢ ((φ ∨ φ) → φ)
2	1	con3i 127	. . 3 ⊢ (¬ φ → ¬ (φ ∨ φ))
3	2	con1i 121	. 2 ⊢ (¬ ¬ (φ ∨ φ) → φ)
4	3	orri 365	1 ⊢ (¬ (φ ∨ φ) ∨ φ)

Syntax hints:  ¬ wn 3   ∨ wo 357

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-or 359

This theorem is referenced by:  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532