Theorem ex-natded9.26-2 27277

Description: A more efficient proof of Theorem 9.26 of [Clemente] p. 45. Compare with ex-natded9.26 27276. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ex-natded9.26.1	|- ( ph -> E. x A. y ps )

Assertion

Ref	Expression
ex-natded9.26-2	|- ( ph -> A. y E. x ps )

Distinct variable group:   x, y, ph

Allowed substitution hints:   ps( x, y)

Proof of Theorem ex-natded9.26-2

Step	Hyp	Ref	Expression
1		ex-natded9.26.1	. . 3 |- ( ph -> E. x A. y ps )
2		sp 2053	. . . 4 |- ( A. y ps -> ps )
3	2	eximi 1762	. . 3 |- ( E. x A. y ps -> E. x ps )
4	1, 3	syl 17	. 2 |- ( ph -> E. x ps )
5	4	alrimiv 1855	1 |- ( ph -> A. y E. x ps )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)