Theorem anmp 1783

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 869	. 2 ⊢ (𝜑 → 𝜓)
4	1, 3	ax-mp 5	1 ⊢ 𝜓

This proof depends on syntax axioms:  ¬ wn 3   ∨ 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-or 862

This theorem is used by:  rbsyl  1788  rblem1  1789  rblem2  1790  rblem4  1792  rblem5  1793  rblem6  1794  rblem7  1795  re1axmp  1796  re2luk1  1797  re2luk2  1798  re2luk3  1799