Theorem bnj1219 30871

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj1219.1	|- ( ch <-> ( ph /\ ps /\ ze ) )
bnj1219.2	|- ( th <-> ( ch /\ ta /\ et ) )

Assertion

Ref	Expression
bnj1219	|- ( th -> ps )

Proof of Theorem bnj1219

Step	Hyp	Ref	Expression
1		bnj1219.2	. 2 |- ( th <-> ( ch /\ ta /\ et ) )
2		bnj1219.1	. . 3 |- ( ch <-> ( ph /\ ps /\ ze ) )
3	2	simp2bi 1077	. 2 |- ( ch -> ps )
4	1, 3	bnj835 30829	1 |- ( th -> ps )

Syntax hints:   -> wi 4   <-> wb 196   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  bnj1379  30901