Theorem cbvmo 1034

Description: Rule used to change bound variables with implicit substitution.

Hypotheses

Ref	Expression
cbvmo.1	|- (ph -> A.yph)
cbvmo.2	|- (ps -> A.xps)
cbvmo.3	|- (x = y -> (ph <-> ps))

Assertion

Ref	Expression
cbvmo	|- (E*xph <-> E*yps)

Distinct variable group(s):   x,y

Proof of Theorem cbvmo

Step	Hyp	Ref	Expression
1		cbvmo.1	. . . 4 |- (ph -> A.yph)
2		cbvmo.2	. . . 4 |- (ps -> A.xps)
3		cbvmo.3	. . . 4 |- (x = y -> (ph <-> ps))
4	1, 2, 3	cbvex 849	. . 3 |- (E.xph <-> E.yps)
5	1, 2, 3	cbveu 1018	. . 3 |- (E!xph <-> E!yps)
6	4, 5	imbi12i 163	. 2 |- ((E.xph -> E!xph) <-> (E.yps -> E!yps))
7		df-mo 1010	. 2 |- (E*xph <-> (E.xph -> E!xph))
8		df-mo 1010	. 2 |- (E*yps <-> (E.yps -> E!yps))
9	6, 7, 8	3bitr4 158	1 |- (E*xph <-> E*yps)

Syntax hints:   -> wi 2   <-> wb 127  A.wal 672  E.wex 678   = weq 797  E!weu 1007  E*wmo 1008

This theorem is referenced by:  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-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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