Theorem equs3 1644

Description: Lemma used in proofs of substitution properties. (Contributed by NM, 5-Aug-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 1578	. 2 |- (A.x(x = y -> -. ph) <-> -. E.x(x = y /\ ph))
2	1	con2bii 322	1 |- (E.x(x = y /\ ph) <-> -. A.x(x = y -> -. ph))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358  A.wal 1540  E.wex 1541

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This proof depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is used by:  equs5e  1888  sbn  2062