Theorem 19.26-2 1594

Description: Theorem 19.26 of [Margaris] p. 90 with two quantifiers. (Contributed by NM, 3-Feb-2005.)

Assertion

Ref	Expression
19.26-2	|- (A.xA.y(ph /\ ps) <-> (A.xA.yph /\ A.xA.yps))

Proof of Theorem 19.26-2

Step	Hyp	Ref	Expression
1		19.26 1593	. . 3 |- (A.y(ph /\ ps) <-> (A.yph /\ A.yps))
2	1	albii 1566	. 2 |- (A.xA.y(ph /\ ps) <-> A.x(A.yph /\ A.yps))
3		19.26 1593	. 2 |- (A.x(A.yph /\ A.yps) <-> (A.xA.yph /\ A.xA.yps))
4	2, 3	bitri 240	1 |- (A.xA.y(ph /\ ps) <-> (A.xA.yph /\ A.xA.yps))

This proof depends on syntax axioms:   <-> wb 176   /\ wa 358  A.wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  opelopabt  4700  fun11  5160