Theorem re1axmp 1529

Description: ax-mp 5 derived from Russell-Bernays'. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
re1axmp.min	⊢ φ
re1axmp.maj	⊢ (φ → ψ)

Assertion

Ref	Expression
re1axmp	⊢ ψ

Proof of Theorem re1axmp

Step	Hyp	Ref	Expression
1		re1axmp.min	. 2 ⊢ φ
2		re1axmp.maj	. . 3 ⊢ (φ → ψ)
3		rb-imdf 1515	. . . 4 ⊢ ¬ (¬ (¬ (φ → ψ) ∨ (¬ φ ∨ ψ)) ∨ ¬ (¬ (¬ φ ∨ ψ) ∨ (φ → ψ)))
4	3	rblem6 1527	. . 3 ⊢ (¬ (φ → ψ) ∨ (¬ φ ∨ ψ))
5	2, 4	anmp 1516	. 2 ⊢ (¬ φ ∨ ψ)
6	1, 5	anmp 1516	1 ⊢ ψ

Syntax hints:  ¬ wn 3   → wi 4   ∨ 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  df-an 360

This theorem is referenced by: (None)