Theorem orfa1 33886

Description: Add a contradicting disjunct to an antecedent. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypothesis

Ref	Expression
orfa1.1	|- ( ph -> ps )

Assertion

Ref	Expression
orfa1	|- ( ( ph \/ F. ) -> ps )

Proof of Theorem orfa1

Step	Hyp	Ref	Expression
1		orfa1.1	. 2 |- ( ph -> ps )
2		falim 1498	. 2 |- ( F. -> ps )
3	1, 2	jaoi 394	1 |- ( ( ph \/ F. ) -> ps )

Syntax hints:   -> wi 4   \/ wo 383   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-or 385  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)