rb-imdf - Metamath Proof Explorer

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Theorem rb-imdf 1675

Description: The definition of implication, in terms of $\/$ and

. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
rb-imdf	$\/$ $\/$ $\/$ $\/$ $\/$

**Proof of Theorem rb-imdf**
Step	Hyp	Ref	Expression
1		imor 428	. 2 $\/$
2		rb-bijust 1674	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
3	1, 2	mpbi 220	1 $\/$ $\/$ $\/$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 196 $\/$ wo 383

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 197 df-or 385

This theorem is referenced by: re1axmp 1689 re2luk1 1690 re2luk2 1691 re2luk3 1692