Theorem equs3 1147

Description: Lemma used in proofs of substitution properties.

Assertion

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

Proof of Theorem equs3

Step	Hyp	Ref	Expression
1		alinexa 1040	. 2 |- (A.x(x = y -> -. ph) <-> -. E.x(x = y /\ ph))
2	1	con2bii 221	1 |- (E.x(x = y /\ ph) <-> -. A.x(x = y -> -. ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   /\ wa 223  A.wal 952   = wceq 954  E.wex 978

This theorem is referenced by:  equs4 1148  equs5e 1196  sbn 1229

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979

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