Theorem rexbidvALT 3053

Description: Alternate proof of rexbidv 3052, shorter but requires more axioms. (Contributed by NM, 20-Nov-1994.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
rexbidv.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
rexbidvALT	|- ( ph -> ( E. x e. A ps <-> E. x e. A ch ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)   A( x)

Proof of Theorem rexbidvALT

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x ph
2		rexbidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	rexbid 3051	1 |- ( ph -> ( E. x e. A ps <-> E. x e. A ch ) )

Syntax hints:   -> wi 4   <-> wb 196   E.wrex 2913

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-an 386  df-ex 1705  df-nf 1710  df-rex 2918

This theorem is referenced by: (None)