Theorem 19.16 1048

Description: Theorem 19.16 of [Margaris] p. 90.

Hypothesis

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

Assertion

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

Proof of Theorem 19.16

Step	Hyp	Ref	Expression
1		19.15 997	. 2 |- (A.x(ph <-> ps) -> (A.xph <-> A.xps))
2		19.16.1	. . 3 |- (ph -> A.xph)
3	2	19.3 1031	. 2 |- (A.xph <-> ph)
4	1, 3	syl5bbr 534	1 |- (A.x(ph <-> ps) -> (ph <-> A.xps))

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

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

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