Theorem 19.37 759

Description: Theorem 19.37 of [Margaris] p. 90.

Hypothesis

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

Assertion

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

Proof of Theorem 19.37

Step	Hyp	Ref	Expression
1		19.35 754	. 2 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
2		19.37.1	. . . 4 |- (ph -> A.xph)
3	2	19.3r 714	. . 3 |- (ph <-> A.xph)
4	3	imbi1i 161	. 2 |- ((ph -> E.xps) <-> (A.xph -> E.xps))
5	1, 4	bitr4 154	1 |- (E.x(ph -> ps) <-> (ph -> E.xps))

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

This theorem is referenced by:  19.37v 961

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  df-ex 679

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