Theorem mobid 1406

Description: Formula-building rule for "at most one" quantifier (deduction rule).

Hypotheses

Ref	Expression
mobid.1	|- (ph -> A.xph)
mobid.2	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
mobid	|- (ph -> (E*xps <-> E*xch))

Proof of Theorem mobid

Step	Hyp	Ref	Expression
1		mobid.1	. . . 4 |- (ph -> A.xph)
2		mobid.2	. . . 4 |- (ph -> (ps <-> ch))
3	1, 2	exbid 1107	. . 3 |- (ph -> (E.xps <-> E.xch))
4	1, 2	eubid 1387	. . 3 |- (ph -> (E!xps <-> E!xch))
5	3, 4	imbi12d 628	. 2 |- (ph -> ((E.xps -> E!xps) <-> (E.xch -> E!xch)))
6		df-mo 1385	. 2 |- (E*xps <-> (E.xps -> E!xps))
7		df-mo 1385	. 2 |- (E*xch <-> (E.xch -> E!xch))
8	5, 6, 7	3bitr4g 557	1 |- (ph -> (E*xps <-> E*xch))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 956  E.wex 982  E!weu 1382  E*wmo 1383

This theorem is referenced by:  mobii 1407  mosubopt 2810  dffunmof 3536  2ndconst 4103  brdom3 4811  brdom7disj 4814  brdom6disj 4815  adjbdlnt 10011

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-eu 1384  df-mo 1385

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