Theorem bnj52 12427

Description: First-order logic and set theory.

Hypotheses

Ref	Expression
bnj52.1	|- -. ph
bnj52.2	|- ((ps /\ -. th) -> ph)

Assertion

Ref	Expression
bnj52	|- (ps -> th)

Proof of Theorem bnj52

Step	Hyp	Ref	Expression
1		bnj52.1	. . 3 |- -. ph
2		bnj52.2	. . 3 |- ((ps /\ -. th) -> ph)
3	1, 2	mto 121	. 2 |- -. (ps /\ -. th)
4		iman 256	. 2 |- ((ps -> th) <-> -. (ps /\ -. th))
5	3, 4	mpbir 207	1 |- (ps -> th)

Syntax hints:  -. wn 2   -> wi 3   /\ wa 240

This theorem is referenced by:  bnj12 13194  bnj56 13195

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

Copyright terms: Public domain