Theorem 2albidv 1920

Description: Formula-building rule for 2 existential quantifiers (deduction form). (Contributed by NM, 4-Mar-1997.)

Hypothesis

Ref	Expression
2albidv.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
2albidv	|- ( ph -> ( A. x A. y ps <-> A. x A. y ch ) )

Distinct variable groups:   ph, x   ph, y

Allowed substitution hints:   ps( x, y)   ch( x, y)

Proof of Theorem 2albidv

Step	Hyp	Ref	Expression
1		2albidv.1	. . 3 |- ( ph -> ( ps <-> ch ) )
2	1	albidv 1877	. 2 |- ( ph -> ( A. y ps <-> A. y ch ) )
3	2	albidv 1877	1 |- ( ph -> ( A. x A. y ps <-> A. x A. y ch ) )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105   A.wal 1400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-17 1579

This proof depends on definitions:  df-bi 117

This theorem is used by:  dff13  5974  qliftfun  6891  seqf1og  10958