Theorem alim 1340

Description: Theorem 19.20 of [Margaris] p. 90. (The proof was shortened by O'Cat, 30-Mar-2008.)

Assertion

Ref	Expression
alim	|- (A.x(ph -> ps) -> (A.xph -> A.xps))

Proof of Theorem alim

Step	Hyp	Ref	Expression
1		id 73	. . . 4 |- ((ph -> ps) -> (ph -> ps))
2	1	a4sd 1331	. . 3 |- ((ph -> ps) -> (A.xph -> ps))
3	2	alimi 1338	. 2 |- (A.x(ph -> ps) -> A.x(A.xph -> ps))
4		ax-5o 1321	. 2 |- (A.x(A.xph -> ps) -> (A.xph -> A.xps))
5	3, 4	syl 12	1 |- (A.x(ph -> ps) -> (A.xph -> A.xps))

Syntax hints:   -> wi 3  A.wal 1296

This theorem is referenced by:  al2imi 1341  19.21 1403  19.29OLD 1422  19.30OLD 1437  19.21t 1473  sbal1 1737  mo 1787  2mo 1851  eunex 3500  hbaltg 13874

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

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