Theorem bnj1119 12929

Description: First-order logic and set theory.

Assertion

Ref	Expression
bnj1119	|- (((ph -> ps) /\ (-. ph -> ps)) -> ps)

Proof of Theorem bnj1119

Step	Hyp	Ref	Expression
1		pm4.77 468	. 2 |- (((ph -> ps) /\ (-. ph -> ps)) <-> ((ph \/ -. ph) -> ps))
2		exmid 717	. . 3 |- (ph \/ -. ph)
3		pm3.35 386	. . 3 |- (((ph \/ -. ph) /\ ((ph \/ -. ph) -> ps)) -> ps)
4	2, 3	mpan 759	. 2 |- (((ph \/ -. ph) -> ps) -> ps)
5	1, 4	sylbi 216	1 |- (((ph -> ps) /\ (-. ph -> ps)) -> ps)

Syntax hints:  -. wn 2   -> wi 3   \/ wo 239   /\ wa 240

This theorem is referenced by:  bnj1120 12930

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-or 241  df-an 242

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