Theorem eqs3 830

Description: Lemma used in proofs of substitution properties.

Assertion

Ref	Expression
eqs3	|- (E.x(x = y /\ ph) <-> -. A.x(x = y -> -. ph))

Proof of Theorem eqs3

Step	Hyp	Ref	Expression
1		alinexa 724	. 2 |- (A.x(x = y -> -. ph) <-> -. E.x(x = y /\ ph))
2	1	bicon2i 194	1 |- (E.x(x = y /\ ph) <-> -. A.x(x = y -> -. ph))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   /\ wa 196  A.wal 672  E.wex 678   = weq 797

This theorem is referenced by:  eqs4 831  eqs5 832  sbn1 880  sbn2 881  sb5y 883

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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