Theorem anmp 1516

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 403	. 2 ⊢ (φ → ψ)
4	1, 3	ax-mp 5	1 ⊢ ψ

Syntax hints:  ¬ wn 3   ∨ 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

This theorem is referenced by:  rbsyl  1521  rblem1  1522  rblem2  1523  rblem4  1525  rblem5  1526  rblem6  1527  rblem7  1528  re1axmp  1529  re2luk1  1530  re2luk2  1531  re2luk3  1532