Theorem 19.19 1055

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 1050	. 2 |- (A.x(ph <-> ps) -> (E.xph <-> E.xps))
2		19.19.1	. . 3 |- (ph -> A.xph)
3	2	19.9 1036	. 2 |- (E.xph <-> ph)
4	1, 3	syl5bbr 534	1 |- (A.x(ph <-> ps) -> (ph <-> E.xps))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 954  E.wex 980

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  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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