Theorem 19.21-2 1056

Description: Theorem 19.21 of [Margaris] p. 90 but with 2 quantifiers.

Hypotheses

Ref	Expression
19.21-2.1	|- (ph -> A.xph)
19.21-2.2	|- (ph -> A.yph)

Assertion

Ref	Expression
19.21-2	|- (A.xA.y(ph -> ps) <-> (ph -> A.xA.yps))

Proof of Theorem 19.21-2

Step	Hyp	Ref	Expression
1		19.21-2.2	. . . 4 |- (ph -> A.yph)
2	1	19.21 1055	. . 3 |- (A.y(ph -> ps) <-> (ph -> A.yps))
3	2	albii 998	. 2 |- (A.xA.y(ph -> ps) <-> A.x(ph -> A.yps))
4		19.21-2.1	. . 3 |- (ph -> A.xph)
5	4	19.21 1055	. 2 |- (A.x(ph -> A.yps) <-> (ph -> A.xA.yps))
6	3, 5	bitr 173	1 |- (A.xA.y(ph -> ps) <-> (ph -> A.xA.yps))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 953

This theorem is referenced by:  2eu6 1453

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-4 972  ax-5o 974  ax-6o 977

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

Copyright terms: Public domain