Theorem 19.34 1663

Description: Theorem 19.34 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.34	|- ((A.xph \/ E.xps) -> E.x(ph \/ ps))

Proof of Theorem 19.34

Step	Hyp	Ref	Expression
1		19.2 1659	. . 3 |- (A.xph -> E.xph)
2	1	orim1i 503	. 2 |- ((A.xph \/ E.xps) -> (E.xph \/ E.xps))
3		19.43 1605	. 2 |- (E.x(ph \/ ps) <-> (E.xph \/ E.xps))
4	2, 3	sylibr 203	1 |- ((A.xph \/ E.xps) -> E.x(ph \/ ps))

Syntax hints:   -> wi 4   \/ wo 357  A.wal 1540  E.wex 1541

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-9 1654

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1542

This theorem is referenced by: (None)