Theorem efald2 33877

Description: A proof by contradiction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypothesis

Ref	Expression
efald2.1	|- ( -. ph -> F. )

Assertion

Ref	Expression
efald2	|- ph

Proof of Theorem efald2

Step	Hyp	Ref	Expression
1		efald2.1	. . . 4 |- ( -. ph -> F. )
2	1	adantl 482	. . 3 |- ( ( T. /\ -. ph ) -> F. )
3	2	efald 1504	. 2 |- ( T. -> ph )
4	3	trud 1493	1 |- ph

Syntax hints:   -. wn 3   -> wi 4   T. wtru 1484   F. wfal 1488

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-tru 1486  df-fal 1489

This theorem is referenced by:  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980