Theorem 19.37 1873

Description: Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.37.1	|- F/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 1600	. 2 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
2		19.37.1	. . . 4 |- F/xph
3	2	19.3 1785	. . 3 |- (A.xph <-> ph)
4	3	imbi1i 315	. 2 |- ((A.xph -> E.xps) <-> (ph -> E.xps))
5	1, 4	bitri 240	1 |- (E.x(ph -> ps) <-> (ph -> E.xps))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540  E.wex 1541   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545

This theorem is referenced by:  19.37v  1899