Theorem 19.26-2 1068

Description: Theorem 19.26 of [Margaris] p. 90 with two quantifiers.

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 1067	. . 3 |- (A.y(ph /\ ps) <-> (A.yph /\ A.yps))
2	1	albii 999	. 2 |- (A.xA.y(ph /\ ps) <-> A.x(A.yph /\ A.yps))
3		19.26 1067	. 2 |- (A.x(A.yph /\ A.yps) <-> (A.xA.yph /\ A.xA.yps))
4	2, 3	bitr 173	1 |- (A.xA.y(ph /\ ps) <-> (A.xA.yph /\ A.xA.yps))

Syntax hints:   <-> wb 146   /\ wa 223  A.wal 954

This theorem is referenced by:  fun11 3562

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain