mpd3an3 - New Foundations Explorer

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Theorem mpd3an3 1278

Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007.)

**Hypotheses**
Ref	Expression
mpd3an3.2	$/\$
mpd3an3.3	$/\$ $/\$

**Assertion**
Ref	Expression
mpd3an3	$/\$

**Proof of Theorem mpd3an3**
Step	Hyp	Ref	Expression
1		mpd3an3.2	. 2 $/\$
2		mpd3an3.3	. . 3 $/\$ $/\$
3	2	3expa 1151	. 2 $/\$ $/\$
4	1, 3	mpdan 649	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 358 $/\$ w3a 934

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936

This theorem is referenced by: nnsucelr 4428 cupvalg 5812 ovcross 5845 pmvalg 6010 enadj 6060 ovmuc 6130 ovce 6172 addlecncs 6209 leconnnc 6218 ncslesuc 6267