Theorem hb3anOLD 1831

Description: Obsolete proof of hb3an 1830 as of 2-Jan-2018. (Contributed by NM, 14-Sep-2003.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
hb.1	|- (ph -> A.xph)
hb.2	|- (ps -> A.xps)
hb.3	|- (ch -> A.xch)

Assertion

Ref	Expression
hb3anOLD	|- ((ph /\ ps /\ ch) -> A.x(ph /\ ps /\ ch))

Proof of Theorem hb3anOLD

Step	Hyp	Ref	Expression
1		df-3an 936	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
2		hb.1	. . . 4 |- (ph -> A.xph)
3		hb.2	. . . 4 |- (ps -> A.xps)
4	2, 3	hban 1828	. . 3 |- ((ph /\ ps) -> A.x(ph /\ ps))
5		hb.3	. . 3 |- (ch -> A.xch)
6	4, 5	hban 1828	. 2 |- (((ph /\ ps) /\ ch) -> A.x((ph /\ ps) /\ ch))
7	1, 6	hbxfrbi 1568	1 |- ((ph /\ ps /\ ch) -> A.x(ph /\ ps /\ ch))

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934  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-3an 936  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)