Theorem drsb2 1793

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.)

Assertion

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

Proof of Theorem drsb2

Step	Hyp	Ref	Expression
1		sbequ 1792	. 2 |- ( x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )
2	1	sps 1498	1 |- ( A. x x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1310   [wsb 1716

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496

This theorem depends on definitions:  df-bi 116  df-nf 1418  df-sb 1717

This theorem is referenced by: (None)