Metamath Proof Explorer


Theorem drsb2

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of Megill p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005)

Ref Expression
Assertion drsb2
|- ( A. x x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )

Proof

Step Hyp Ref Expression
1 sbequ
 |-  ( x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )
2 1 sps
 |-  ( A. x x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )