Theorem sbequ8ALT 2256

Description: Alternate proof of sbequ8 1810, shorter but requiring more axioms. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
sbequ8ALT	|- ( [ y / x ] ph <-> [ y / x ] ( x = y -> ph ) )

Proof of Theorem sbequ8ALT

Step	Hyp	Ref	Expression
1		equsb1 2217	. . 3 |- [ y / x ] x = y
2	1	a1bi 344	. 2 |- ( [ y / x ] ph <-> ( [ y / x ] x = y -> [ y / x ] ph ) )
3		sbim 2244	. 2 |- ( [ y / x ] ( x = y -> ph ) <-> ( [ y / x ] x = y -> [ y / x ] ph ) )
4	2, 3	bitr4i 260	1 |- ( [ y / x ] ph <-> [ y / x ] ( x = y -> ph ) )

Syntax hints:   -> wi 4   <-> wb 189   [wsb 1805

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104

This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806

This theorem is referenced by: (None)