Theorem ccase2 755

Description: Inference for combining cases.

Hypotheses

Ref	Expression
ccase2.1	|- ((ph /\ ps) -> ta)
ccase2.2	|- (ch -> ta)
ccase2.3	|- (th -> ta)

Assertion

Ref	Expression
ccase2	|- (((ph \/ ch) /\ (ps \/ th)) -> ta)

Proof of Theorem ccase2

Step	Hyp	Ref	Expression
1		ccase2.1	. 2 |- ((ph /\ ps) -> ta)
2		ccase2.2	. . 3 |- (ch -> ta)
3	2	adantr 389	. 2 |- ((ch /\ ps) -> ta)
4		ccase2.3	. . 3 |- (th -> ta)
5	4	adantl 388	. 2 |- ((ph /\ th) -> ta)
6	4	adantl 388	. 2 |- ((ch /\ th) -> ta)
7	1, 3, 5, 6	ccase 753	1 |- (((ph \/ ch) /\ (ps \/ th)) -> ta)

Syntax hints:   -> wi 3   \/ wo 222   /\ wa 223

This theorem is referenced by:  add20 5576  mulge0 5581  nn0mulcl 6069  bccl2t 6909  fctop 7592  cctop 7594

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 147  df-or 224  df-an 225

Copyright terms: Public domain