Theorem mobid 2303

Description: Formula-building rule for "at most one" quantifier (deduction rule). (Contributed by NM, 8-Mar-1995.)

Hypotheses

Ref	Expression
mobid.1
mobid.2

Assertion

Ref	Expression
mobid

Proof of Theorem mobid

Step	Hyp	Ref	Expression
1		mobid.1	. . . 4
2		mobid.2	. . . 4
3	1, 2	exbid 1886	. . 3
4	1, 2	eubid 2302	. . 3
5	3, 4	imbi12d 320	. 2
6		df-mo 2287	. 2
7		df-mo 2287	. 2
8	5, 6, 7	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  E.wex 1612  F/wnf 1616  E!weu 2282  E*wmo 2283

This theorem is referenced by:  mobidv  2305  moanim  2350  rmobida  3045  rmoeq1f  3053  funcnvmptOLD  27509  funcnvmpt  27510

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287