Theorem bimod 1030

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

Hypotheses

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

Assertion

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

Proof of Theorem bimod

Step	Hyp	Ref	Expression
1		bimod.1	. . . 4 |- (ph -> A.xph)
2		bimod.2	. . . 4 |- (ph -> (ps <-> ch))
3	1, 2	biexd 783	. . 3 |- (ph -> (E.xps <-> E.xch))
4	1, 2	bieud 1012	. . 3 |- (ph -> (E!xps <-> E!xch))
5	3, 4	imbi12d 474	. 2 |- (ph -> ((E.xps -> E!xps) <-> (E.xch -> E!xch)))
6		df-mo 1010	. 2 |- (E*xps <-> (E.xps -> E!xps))
7		df-mo 1010	. 2 |- (E*xch <-> (E.xch -> E!xch))
8	5, 6, 7	3bitr4g 428	1 |- (ph -> (E*xps <-> E*xch))

Syntax hints:   -> wi 2   <-> wb 127  A.wal 672  E.wex 678  E!weu 1007  E*wmo 1008

This theorem is referenced by:  bimo 1031  mosubop 1911  dffunmof 2678

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-eu 1009  df-mo 1010

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