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Theorem nic-stdmp 1455

Description: Derive the standard modus ponens from nic-mp 1436. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

**Hypotheses**
Ref	Expression
nic-smin
nic-smaj

**Assertion**
Ref	Expression
nic-stdmp

**Proof of Theorem nic-stdmp**
Step	Hyp	Ref	Expression
1		nic-smin	. 2
2		nic-smaj	. . 3
3		nic-dfim 1434	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	3	nic-bi2 1454	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
5	2, 4	nic-mp 1436	. 2 $-/\$ $-/\$
6	1, 5	nic-mp 1436	1

Colors of variables: wff setvar class

Syntax hints:

wi 4 $-/\$ wnan 1287

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 df-nan 1288

This theorem is referenced by: (None)

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