Theorem 19.26-2 1064

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 1063	. . 3 |- (A.y(ph /\ ps) <-> (A.yph /\ A.yps))
2	1	albii 996	. 2 |- (A.xA.y(ph /\ ps) <-> A.x(A.yph /\ A.yps))
3		19.26 1063	. 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 951

This theorem is referenced by:  fun11 3548

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972

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

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