Theorem 19.37 1080

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 1075	. 2 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
2		19.37.1	. . . 4 |- (ph -> A.xph)
3	2	19.3 1031	. . 3 |- (A.xph <-> ph)
4	3	imbi1i 186	. 2 |- ((A.xph -> E.xps) <-> (ph -> E.xps))
5	1, 4	bitr 173	1 |- (E.x(ph -> ps) <-> (ph -> E.xps))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 954  E.wex 980

This theorem is referenced by:  19.37v 1303

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  df-ex 981

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