Theorem 19.45 1086

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 1084	. 2 |- (E.x(ph \/ ps) <-> (E.xph \/ E.xps))
2		19.45.1	. . . 4 |- (ph -> A.xph)
3	2	19.9 1032	. . 3 |- (E.xph <-> ph)
4	3	orbi1i 256	. 2 |- ((E.xph \/ E.xps) <-> (ph \/ E.xps))
5	1, 4	bitr 173	1 |- (E.x(ph \/ ps) <-> (ph \/ E.xps))

Syntax hints:   -> wi 3   <-> wb 146   \/ wo 222  A.wal 951  E.wex 977

This theorem is referenced by:  eeor 1116  iununi 2606

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978

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