Theorem equs3 1875

Description: Lemma used in proofs of substitution properties. (Contributed by NM, 10-May-1993.)

Assertion

Ref	Expression
equs3	|- ( E. x ( x = y /\ ph ) <-> -. A. x ( x = y -> -. ph ) )

Proof of Theorem equs3

Step	Hyp	Ref	Expression
1		alinexa 1770	. 2 |- ( A. x ( x = y -> -. ph ) <-> -. E. x ( x = y /\ ph ) )
2	1	con2bii 347	1 |- ( E. x ( x = y /\ ph ) <-> -. A. x ( x = y -> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)