nic-stdmp - Metamath Proof Explorer

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Theorem nic-stdmp 1256

Description: Derive the standard modus ponens from nic-mp 1237. (Contributed by Jeff Hoffman, 18-Nov-2007.)

**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 1235	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	3	nic-bi2 1255	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
5	2, 4	nic-mp 1237	. 2 $-/\$ $-/\$
6	1, 5	nic-mp 1237	1

Colors of variables: wff set class

Syntax hints:

wi 3 $-/\$ wnand 1229

This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7

This theorem depends on definitions: df-bi 164 df-or 241 df-an 242 df-nand 1230