Theorem rb-ax3 1757

Description: The third 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-ax3	⊢ (¬ 𝜑 ∨ (𝜓 ∨ 𝜑))

Proof of Theorem rb-ax3

Step	Hyp	Ref	Expression
1		pm2.46 880	. . 3 ⊢ (¬ (𝜓 ∨ 𝜑) → ¬ 𝜑)
2	1	con1i 147	. 2 ⊢ (¬ ¬ 𝜑 → (𝜓 ∨ 𝜑))
3	2	orri 859	1 ⊢ (¬ 𝜑 ∨ (𝜓 ∨ 𝜑))

Syntax hints:  ¬ wn 3   ∨ wo 844

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 206  df-or 845

This theorem is referenced by:  rblem2  1761  rblem4  1763  rblem5  1764  rblem6  1765  rblem7  1766  re2luk1  1768  re2luk2  1769  re2luk3  1770