Theorem 19.36i 1081

Description: Inference from Theorem 19.36 of [Margaris] p. 90.

Hypotheses

Ref	Expression
19.36i.1	|- (ps -> A.xps)
19.36i.2	|- E.x(ph -> ps)

Assertion

Ref	Expression
19.36i	|- (A.xph -> ps)

Proof of Theorem 19.36i

Step	Hyp	Ref	Expression
1		19.36i.2	. 2 |- E.x(ph -> ps)
2		19.36i.1	. . 3 |- (ps -> A.xps)
3	2	19.36 1080	. 2 |- (E.x(ph -> ps) <-> (A.xph -> ps))
4	1, 3	mpbi 189	1 |- (A.xph -> ps)

Syntax hints:   -> wi 3  A.wal 956  E.wex 982

This theorem is referenced by:  19.36aiv 1303  vtoclf 1844

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

Copyright terms: Public domain