Theorem 19.15 997

Description: Theorem 19.15 of [Margaris] p. 90.

Assertion

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

Proof of Theorem 19.15

Step	Hyp	Ref	Expression
1		bi1 148	. . 3 |- ((ph <-> ps) -> (ph -> ps))
2	1	19.20ii 995	. 2 |- (A.x(ph <-> ps) -> (A.xph -> A.xps))
3		bi2 149	. . 3 |- ((ph <-> ps) -> (ps -> ph))
4	3	19.20ii 995	. 2 |- (A.x(ph <-> ps) -> (A.xps -> A.xph))
5	2, 4	impbid 516	1 |- (A.x(ph <-> ps) -> (A.xph <-> A.xps))

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

This theorem is referenced by:  albii 999  19.16 1048  19.17 1049  19.33b 1092  albid 1104  intmin4 2559

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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