Theorem a12stdy3 1351

Description: Part of a study related to ax-12 1104. The consequent introduces two new variables. There are no distinct variable restrictions.

Assertion

Ref	Expression
a12stdy3	|- (A.z(z = x /\ x = y) -> A.vE.y x = w)

Proof of Theorem a12stdy3

Step	Hyp	Ref	Expression
1		a12stdy2 1350	. 2 |- (A.z(z = x /\ x = y) -> A.y y = x)
2		hbae 1128	. 2 |- (A.y y = x -> A.vA.y y = x)
3		a12stdy1 1349	. . 3 |- (A.y y = x -> E.y x = w)
4	3	19.20i 968	. 2 |- (A.vA.y y = x -> A.vE.y x = w)
5	1, 2, 4	3syl 20	1 |- (A.z(z = x /\ x = y) -> A.vE.y x = w)

Syntax hints:   -> wi 3   /\ wa 223  A.wal 950  E.wex 956   = wceq 1099

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955  ax-8 1101  ax-9 1102  ax-10 1103  ax-12 1104

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957

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