Theorem 19.36 1074

Description: Theorem 19.36 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.36.1	|- (ps -> A.xps)

Assertion

Ref	Expression
19.36	|- (E.x(ph -> ps) <-> (A.xph -> ps))

Proof of Theorem 19.36

Step	Hyp	Ref	Expression
1		19.35 1071	. 2 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
2		19.36.1	. . . 4 |- (ps -> A.xps)
3	2	19.9 1032	. . 3 |- (E.xps <-> ps)
4	3	imbi2i 185	. 2 |- ((A.xph -> E.xps) <-> (A.xph -> ps))
5	1, 4	bitr 173	1 |- (E.x(ph -> ps) <-> (A.xph -> ps))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 951  E.wex 977

This theorem is referenced by:  19.36i 1075  19.36v 1295  cla4gf 1851

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978

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