Theorem 19.19 737

Description: Theorem 19.19 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.19.1	|- (ph -> A.xph)

Assertion

Ref	Expression
19.19	|- (A.x(ph <-> ps) -> (ph <-> E.xps))

Proof of Theorem 19.19

Step	Hyp	Ref	Expression
1		19.18 732	. 2 |- (A.x(ph <-> ps) -> (E.xph <-> E.xps))
2		19.19.1	. . 3 |- (ph -> A.xph)
3	2	19.9r 718	. 2 |- (ph <-> E.xph)
4	1, 3	syl5bb 410	1 |- (A.x(ph <-> ps) -> (ph <-> E.xps))

Syntax hints:   -> wi 2   <-> wb 127  A.wal 672  E.wex 678

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

metamath.org