Theorem pm3.2an3 1049

Description: pm3.2 305 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)

Assertion

Ref	Expression
pm3.2an3	|- (ph -> (ps -> (ch -> (ph /\ ps /\ ch))))

Proof of Theorem pm3.2an3

Step	Hyp	Ref	Expression
1		pm3.2 305	. . 3 |- ((ph /\ ps) -> (ch -> ((ph /\ ps) /\ ch)))
2	1	ex 402	. 2 |- (ph -> (ps -> (ch -> ((ph /\ ps) /\ ch))))
3		df-3an 860	. . 3 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
4	3	bicomi 189	. 2 |- (((ph /\ ps) /\ ch) <-> (ph /\ ps /\ ch))
5	2, 4	syl8ib 234	1 |- (ph -> (ps -> (ch -> (ph /\ ps /\ ch))))

Syntax hints:   -> wi 3   /\ wa 240   /\ w3a 858

This theorem is referenced by:  tratrb 5831  intcont 14914  19.21a3con13vVD 16676  tratrbVD 16685

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-3an 860

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