Theorem hbanOLD 1829

Description: Obsolete proof of hban 1828 as of 2-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
hb.1	|- (ph -> A.xph)
hb.2	|- (ps -> A.xps)

Assertion

Ref	Expression
hbanOLD	|- ((ph /\ ps) -> A.x(ph /\ ps))

Proof of Theorem hbanOLD

Step	Hyp	Ref	Expression
1		df-an 360	. 2 |- ((ph /\ ps) <-> -. (ph -> -. ps))
2		hb.1	. . . 4 |- (ph -> A.xph)
3		hb.2	. . . . 5 |- (ps -> A.xps)
4	3	hbn 1776	. . . 4 |- (-. ps -> A.x -. ps)
5	2, 4	hbim 1817	. . 3 |- ((ph -> -. ps) -> A.x(ph -> -. ps))
6	5	hbn 1776	. 2 |- (-. (ph -> -. ps) -> A.x -. (ph -> -. ps))
7	1, 6	hbxfrbi 1568	1 |- ((ph /\ ps) -> A.x(ph /\ ps))

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)