Theorem bnj1359 13084

Description: First-order logic and set theory.

Hypotheses

Ref	Expression
bnj1359.1	|- (ph <-> (ps /\ ch))
bnj1359.2	|- (ph -> th)

Assertion

Ref	Expression
bnj1359	|- (ps -> (ch -> th))

Proof of Theorem bnj1359

Step	Hyp	Ref	Expression
1		bnj1359.1	. . 3 |- (ph <-> (ps /\ ch))
2		bnj1359.2	. . 3 |- (ph -> th)
3	1, 2	sylbir 218	. 2 |- ((ps /\ ch) -> th)
4	3	ex 402	1 |- (ps -> (ch -> th))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem is referenced by:  bnj1336 13088  bnj513 13254  bnj578 13291  bnj605 13292  bnj607 13304  bnj1016 13376  bnj1175 13443  bnj1398 13515  bnj1404 13517  bnj1440 13543

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