Theorem hbmo 1406

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 1005	. . 3 |- (E.yph -> A.xE.yph)
3	1	hbeu 1388	. . 3 |- (E!yph -> A.xE!yph)
4	2, 3	hbim 1006	. 2 |- ((E.yph -> E!yph) -> A.x(E.yph -> E!yph))
5		df-mo 1382	. 2 |- (E*yph <-> (E.yph -> E!yph))
6	5	albii 998	. 2 |- (A.xE*yph <-> A.x(E.yph -> E!yph))
7	4, 5, 6	3imtr4 219	1 |- (E*yph -> A.xE*yph)

Syntax hints:   -> wi 3  A.wal 953  E.wex 979  E!weu 1379  E*wmo 1380

This theorem is referenced by:  moexex 1437  2moex 1439  2euex 1440  2exeu 1445  mosubopt 2800  dffunmof 3526

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-eu 1381  df-mo 1382

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