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Theorem orbi2d 682

Description: Deduction adding a left disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)

**Hypothesis**
Ref	Expression
bid.1

**Assertion**
Ref	Expression
orbi2d	$\/$ $\/$

**Proof of Theorem orbi2d**
Step	Hyp	Ref	Expression
1		bid.1	. . 3
2	1	imbi2d 307	. 2
3		df-or 359	. 2 $\/$
4		df-or 359	. 2 $\/$
5	2, 3, 4	3bitr4g 279	1 $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 176 $\/$ wo 357

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-or 359

This theorem is referenced by: orbi1d 683 orbi12d 690 cad1 1398 eueq2 3010 sbc2or 3054 rexprg 3776 rextpg 3778 clos1basesucg 5884 nc0suc 6217 nmembers1lem3 6270