dedlemb - Metamath Proof Explorer

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Theorem dedlemb 1003

Description: Lemma for weak deduction theorem. See also ifpfal 1024. (Contributed by NM, 15-May-1999.) (Proof shortened by Andrew Salmon, 7-May-2011.)

**Assertion**
Ref	Expression
dedlemb	$/\$ $\/$ $/\$

**Proof of Theorem dedlemb**
Step	Hyp	Ref	Expression
1		olc 399	. . 3 $/\$ $/\$ $\/$ $/\$
2	1	expcom 451	. 2 $/\$ $\/$ $/\$
3		pm2.21 120	. . . 4
4	3	adantld 483	. . 3 $/\$
5		simpl 473	. . . 4 $/\$
6	5	a1i 11	. . 3 $/\$
7	4, 6	jaod 395	. 2 $/\$ $\/$ $/\$
8	2, 7	impbid 202	1 $/\$ $\/$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 196 $\/$ wo 383 $/\$ wa 384

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

This theorem is referenced by: pm4.42 1004 elimhOLD 1033 iffalse 4095

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