Theorem drsb2 1894

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 1893	. 2 |- ( x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )
2	1	sps 1590	1 |- ( A. x x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1400   [wsb 1815

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816

This theorem is referenced by: (None)