Theorem bnj1254 30880

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

Hypothesis

Ref	Expression
bnj1254.1	|- ( ph <-> ( ps /\ ch /\ th /\ ta ) )

Assertion

Ref	Expression
bnj1254	|- ( ph -> ta )

Proof of Theorem bnj1254

Step	Hyp	Ref	Expression
1		bnj1254.1	. 2 |- ( ph <-> ( ps /\ ch /\ th /\ ta ) )
2		id 22	. . 3 |- ( ta -> ta )
3	2	bnj708 30826	. 2 |- ( ( ps /\ ch /\ th /\ ta ) -> ta )
4	1, 3	sylbi 207	1 |- ( ph -> ta )

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-bnj17 30753

This theorem is referenced by:  bnj554  30969  bnj557  30971  bnj967  31015  bnj999  31027  bnj907  31035  bnj1118  31052  bnj1128  31058  bnj1253  31085  bnj1450  31118