Theorem bnj1232 30874

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

Hypothesis

Ref	Expression
bnj1232.1	|- ( ph <-> ( ps /\ ch /\ th /\ ta ) )

Assertion

Ref	Expression
bnj1232	|- ( ph -> ps )

Proof of Theorem bnj1232

Step	Hyp	Ref	Expression
1		bnj1232.1	. 2 |- ( ph <-> ( ps /\ ch /\ th /\ ta ) )
2		bnj642 30818	. 2 |- ( ( ps /\ ch /\ th /\ ta ) -> ps )
3	1, 2	sylbi 207	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   <-> wb 196   /\ w-bnj17 30752

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  df-bnj17 30753

This theorem is referenced by:  bnj605  30977  bnj607  30986  bnj944  31008  bnj969  31016  bnj970  31017  bnj1001  31028  bnj1110  31050  bnj1118  31052  bnj1128  31058  bnj1145  31061  bnj1311  31092