Theorem anmp 1667

Description: Modus ponens for ∨ ¬ axiom systems. (Contributed by Anthony Hart, 12-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
anmp.min	⊢ 𝜑
anmp.maj	⊢ (¬ 𝜑 ∨ 𝜓)

Assertion

Ref	Expression
anmp	⊢ 𝜓

Proof of Theorem anmp

Step	Hyp	Ref	Expression
1		anmp.min	. 2 ⊢ 𝜑
2		anmp.maj	. . 3 ⊢ (¬ 𝜑 ∨ 𝜓)
3	2	imorri 429	. 2 ⊢ (𝜑 → 𝜓)
4	1, 3	ax-mp 5	1 ⊢ 𝜓

Syntax hints:  ¬ wn 3   ∨ wo 382

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 196  df-or 384

This theorem is referenced by:  rbsyl  1672  rblem1  1673  rblem2  1674  rblem4  1676  rblem5  1677  rblem6  1678  rblem7  1679  re1axmp  1680  re2luk1  1681  re2luk2  1682  re2luk3  1683