Theorem drsb2 1864

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 1863	. 2 |- ( x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )
2	1	sps 1560	1 |- ( A. x x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1371   [wsb 1785

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786

This theorem is referenced by: (None)