Theorem ax5 976

Description: Rederivation of axiom ax-5 960 from the orginal version, ax-5o 975. See ax5o 974 for the derivation of ax-5o 975 from ax-5 960.

This theorem should not be referenced in any proof. Instead, use ax-5 960 above so that uses of ax-5 960 can be more easily identified.

Assertion

Ref	Expression
ax5	|- (A.x(ph -> ps) -> (A.xph -> A.xps))

Proof of Theorem ax5

Step	Hyp	Ref	Expression
1		ax-4 973	. . . . 5 |- (A.x(ph -> ps) -> (ph -> ps))
2		ax-4 973	. . . . 5 |- (A.xph -> ph)
3	1, 2	syl5 21	. . . 4 |- (A.x(ph -> ps) -> (A.xph -> ps))
4	3	ax-gen 963	. . 3 |- A.x(A.x(ph -> ps) -> (A.xph -> ps))
5		ax-5o 975	. . 3 |- (A.x(A.x(ph -> ps) -> (A.xph -> ps)) -> (A.x(ph -> ps) -> A.x(A.xph -> ps)))
6	4, 5	ax-mp 7	. 2 |- (A.x(ph -> ps) -> A.x(A.xph -> ps))
7		ax-5o 975	. 2 |- (A.x(A.xph -> ps) -> (A.xph -> A.xps))
8	6, 7	syl 10	1 |- (A.x(ph -> ps) -> (A.xph -> A.xps))

Syntax hints:   -> wi 3  A.wal 954

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

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