Theorem a12stdy3 1374

Description: Part of a study related to ax-12 968. 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 1373	. 2 |- (A.z(z = x /\ x = y) -> A.y y = x)
2		hbae 1145	. 2 |- (A.y y = x -> A.vA.y y = x)
3		a12stdy1 1372	. . 3 |- (A.y y = x -> E.y x = w)
4	3	19.20i 992	. 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 954   = wceq 956  E.wex 980

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-9 965  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-10o 1140

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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