Theorem 19.15 694

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 130	. . 3 |- ((ph <-> ps) -> (ph -> ps))
2	1	19.20ii 692	. 2 |- (A.x(ph <-> ps) -> (A.xph -> A.xps))
3		bi2 131	. . 3 |- ((ph <-> ps) -> (ps -> ph))
4	3	19.20ii 692	. 2 |- (A.x(ph <-> ps) -> (A.xps -> A.xph))
5	2, 4	impbid 397	1 |- (A.x(ph <-> ps) -> (A.xph <-> A.xps))

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

This theorem is referenced by:  bial 695  19.16 730  19.17 731  19.33b 771  biald 782  sbal1 996

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-gen 677

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

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