Theorem 19.45 769

Description: Theorem 19.45 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.45.1	|- (ph -> A.xph)

Assertion

Ref	Expression
19.45	|- (E.x(ph \/ ps) <-> (ph \/ E.xps))

Proof of Theorem 19.45

Step	Hyp	Ref	Expression
1		19.43 767	. 2 |- (E.x(ph \/ ps) <-> (E.xph \/ E.xps))
2		19.45.1	. . . 4 |- (ph -> A.xph)
3	2	19.9r 718	. . 3 |- (ph <-> E.xph)
4	3	orbi1i 215	. 2 |- ((ph \/ E.xps) <-> (E.xph \/ E.xps))
5	1, 4	bitr4 154	1 |- (E.x(ph \/ ps) <-> (ph \/ E.xps))

Syntax hints:   -> wi 2   <-> wb 127   \/ wo 195  A.wal 672  E.wex 678

This theorem is referenced by:  eeor 795  iununi 2037

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679

metamath.org