Theorem 19.33 1370

Description: Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem 19.33

Step	Hyp	Ref	Expression
1		orc 632	. . 3 |- (ph -> (ph \/ ps))
2	1	alimi 1341	. 2 |- (A.xph -> A.x(ph \/ ps))
3		olc 631	. . 3 |- (ps -> (ph \/ ps))
4	3	alimi 1341	. 2 |- (A.xps -> A.x(ph \/ ps))
5	2, 4	jaoi 635	1 |- ((A.xph \/ A.xps) -> A.x(ph \/ ps))

Syntax hints:   -> wi 4   \/ wo 628  A.wal 1240

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-gen 1335

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  19.33b2  1517