Theorem dedt 1031

Description: The weak deduction theorem. For more information, see the Weak Deduction Theorem page mmdeduction.html. (Contributed by NM, 26-Jun-2002.) Revised to use the conditional operator. (Revised by BJ, 30-Sep-2019.)

Hypotheses

Ref	Expression
dedt.1	|- ( (if- ( ch , ph , ps ) <-> ph ) -> ( th <-> ta ) )
dedt.2	|- ta

Assertion

Ref	Expression
dedt	|- ( ch -> th )

Proof of Theorem dedt

Step	Hyp	Ref	Expression
1		ifptru 1023	. 2 |- ( ch -> (if- ( ch , ph , ps ) <-> ph ) )
2		dedt.2	. . 3 |- ta
3		dedt.1	. . 3 |- ( (if- ( ch , ph , ps ) <-> ph ) -> ( th <-> ta ) )
4	2, 3	mpbiri 248	. 2 |- ( (if- ( ch , ph , ps ) <-> ph ) -> th )
5	1, 4	syl 17	1 |- ( ch -> th )

Syntax hints:   -> wi 4   <-> wb 196  if-wif 1012

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-or 385  df-an 386  df-ifp 1013

This theorem is referenced by:  con3ALT  1032