Theorem alcoms 2035

Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993.)

Hypothesis

Ref	Expression
alcoms.1	|- ( A. x A. y ph -> ps )

Assertion

Ref	Expression
alcoms	|- ( A. y A. x ph -> ps )

Proof of Theorem alcoms

Step	Hyp	Ref	Expression
1		ax-11 2034	. 2 |- ( A. y A. x ph -> A. x A. y ph )
2		alcoms.1	. 2 |- ( A. x A. y ph -> ps )
3	1, 2	syl 17	1 |- ( A. y A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-11 2034

This theorem is referenced by:  cbv2h  2269  mo3  2507  bj-nfalt  32702  bj-cbv3ta  32710  bj-cbv2hv  32731  bj-mo3OLD  32832  wl-equsal1i  33329  wl-mo3t  33358  axc11n-16  34223  axc11next  38607