Metamath Proof Explorer


Theorem sb5OLD

Description: Obsolete version of sb5 as of 4-Sep-2023.) (Contributed by NM, 18-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion sb5OLD
|- ( [ y / x ] ph <-> E. x ( x = y /\ ph ) )

Proof

Step Hyp Ref Expression
1 sb6
 |-  ( [ y / x ] ph <-> A. x ( x = y -> ph ) )
2 sb56
 |-  ( E. x ( x = y /\ ph ) <-> A. x ( x = y -> ph ) )
3 1 2 bitr4i
 |-  ( [ y / x ] ph <-> E. x ( x = y /\ ph ) )