Theorem eqs4 831

Description: Lemma used in proofs of substitution properties.

Assertion

Ref	Expression
eqs4	|- (A.x(x = y -> ph) -> E.x(x = y /\ ph))

Proof of Theorem eqs4

Step	Hyp	Ref	Expression
1		eqs1 828	. 2 |- (A.x(x = y -> ph) -> -. A.x(x = y -> -. ph))
2		eqs3 830	. 2 |- (E.x(x = y /\ ph) <-> -. A.x(x = y -> -. ph))
3	1, 2	sylibr 175	1 |- (A.x(x = y -> ph) -> E.x(x = y /\ ph))

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

This theorem is referenced by:  sb2 859  alexeq 1409

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-6 675  ax-gen 677  ax-9 799

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

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