Theorem bnj32 12398

Description: First-order logic and set theory. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
bnj32	|- (A.x(ps -> ch) -> (E.x e. A ps -> E.x e. A ch))

Proof of Theorem bnj32

Step	Hyp	Ref	Expression
1		hba1 1350	. 2 |- (A.x(ps -> ch) -> A.xA.x(ps -> ch))
2		ax-4 1319	. . 3 |- (A.x(ps -> ch) -> (ps -> ch))
3	2	a1d 15	. 2 |- (A.x(ps -> ch) -> (x e. A -> (ps -> ch)))
4	1, 3	reximdai 2199	1 |- (A.x(ps -> ch) -> (E.x e. A ps -> E.x e. A ch))

Syntax hints:   -> wi 3  A.wal 1296   e. wcel 1300  E.wrex 2106

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-ral 2109  df-rex 2110

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