Theorem bj-sbidmOLD 32831

Description: Obsolete proof of sbidm 2414 temporarily kept here to check it gives no additional insight. (Contributed by NM, 8-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
bj-sbidmOLD	|- ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph )

Proof of Theorem bj-sbidmOLD

Step	Hyp	Ref	Expression
1		equsb2 2369	. . 3 |- [ y / x ] y = x
2		sbequ12r 2112	. . . 4 |- ( y = x -> ( [ y / x ] ph <-> ph ) )
3	2	sbimi 1886	. . 3 |- ( [ y / x ] y = x -> [ y / x ] ( [ y / x ] ph <-> ph ) )
4	1, 3	ax-mp 5	. 2 |- [ y / x ] ( [ y / x ] ph <-> ph )
5		sbbi 2401	. 2 |- ( [ y / x ] ( [ y / x ] ph <-> ph ) <-> ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph ) )
6	4, 5	mpbi 220	1 |- ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph )

Syntax hints:   <-> wb 196   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)