Theorem 19.44 1089

Description: Theorem 19.44 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.44.1	|- (ps -> A.xps)

Assertion

Ref	Expression
19.44	|- (E.x(ph \/ ps) <-> (E.xph \/ ps))

Proof of Theorem 19.44

Step	Hyp	Ref	Expression
1		19.43 1088	. 2 |- (E.x(ph \/ ps) <-> (E.xph \/ E.xps))
2		19.44.1	. . . 4 |- (ps -> A.xps)
3	2	19.9 1036	. . 3 |- (E.xps <-> ps)
4	3	orbi2i 255	. 2 |- ((E.xph \/ E.xps) <-> (E.xph \/ ps))
5	1, 4	bitr 173	1 |- (E.x(ph \/ ps) <-> (E.xph \/ ps))

Syntax hints:   -> wi 3   <-> wb 146   \/ wo 222  A.wal 954  E.wex 980

This theorem is referenced by:  eeor 1120  grothprim 8783

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  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981

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