Theorem re1axmp 1797

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 1783	. . . 4 ⊢ ¬ (¬ (¬ (𝜑 → 𝜓) ∨ (¬ 𝜑 ∨ 𝜓)) ∨ ¬ (¬ (¬ 𝜑 ∨ 𝜓) ∨ (𝜑 → 𝜓)))
4	3	rblem6 1795	. . 3 ⊢ (¬ (𝜑 → 𝜓) ∨ (¬ 𝜑 ∨ 𝜓))
5	2, 4	anmp 1784	. 2 ⊢ (¬ 𝜑 ∨ 𝜓)
6	1, 5	anmp 1784	1 ⊢ 𝜓

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

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

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by: (None)