Theorem rbsyl 1521

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
rbsyl.1	⊢ (¬ ψ ∨ χ)
rbsyl.2	⊢ (φ ∨ ψ)

Assertion

Ref	Expression
rbsyl	⊢ (φ ∨ χ)

Proof of Theorem rbsyl

Step	Hyp	Ref	Expression
1		rbsyl.2	. 2 ⊢ (φ ∨ ψ)
2		rbsyl.1	. . 3 ⊢ (¬ ψ ∨ χ)
3		rb-ax1 1517	. . 3 ⊢ (¬ (¬ ψ ∨ χ) ∨ (¬ (φ ∨ ψ) ∨ (φ ∨ χ)))
4	2, 3	anmp 1516	. 2 ⊢ (¬ (φ ∨ ψ) ∨ (φ ∨ χ))
5	1, 4	anmp 1516	1 ⊢ (φ ∨ χ)

This proof depends on syntax axioms:  ¬ wn 3   ∨ 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  df-an 360

This theorem is used by:  rblem1  1522  rblem2  1523  rblem3  1524  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532