Theorem hbmo 1033

Description: Bound-variable hypothesis builder for "at most one".

Hypothesis

Ref	Expression
hbmo.1	|- (ph -> A.xph)

Assertion

Ref	Expression
hbmo	|- (E*yph -> A.xE*yph)

Proof of Theorem hbmo

Step	Hyp	Ref	Expression
1		hbmo.1	. . . 4 |- (ph -> A.xph)
2	1	hbex 701	. . 3 |- (E.yph -> A.xE.yph)
3	1	hbeu 1016	. . 3 |- (E!yph -> A.xE!yph)
4	2, 3	hbim 702	. 2 |- ((E.yph -> E!yph) -> A.x(E.yph -> E!yph))
5		df-mo 1010	. 2 |- (E*yph <-> (E.yph -> E!yph))
6	5	bial 695	. 2 |- (A.xE*yph <-> A.x(E.yph -> E!yph))
7	4, 5, 6	3imtr4 192	1 |- (E*yph -> A.xE*yph)

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

This theorem is referenced by:  moexex 1058  2moex 1060  2euex 1061  2exeu 1066  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-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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