New Foundations Explorer		< Previous   Next > Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  mpcom		Unicode version

---

Theorem mpcom 32

Description: Modus ponens inference with commutation of antecedents. (Contributed by NM, 17-Mar-1996.)

Hypotheses

Ref	Expression
mpcom.1
mpcom.2

Assertion

Ref	Expression
mpcom

---

Proof of Theorem mpcom

Step	Hyp	Ref	Expression
1		mpcom.1	. 2
2		mpcom.2	. . 3
3	2	com12 27	. 2
4	1, 3	mpd 14	1

Colors of variables: wff setvar class

Syntax hints:   wi 4

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

This theorem is referenced by:  syldan  456  ax16i  2046  ceqex  2969  unsneqsn  3887  sfintfin  4532  0cnelphi  4597  vtoclr  4816  opeldm  4910  tz6.12-1  5344  tz6.12c  5347  fununiq  5517  oprabid  5550  eloprabga  5578  ndmovordi  5621  clos1conn  5879  enmap2lem3  6065  enmap2  6068  enmap1lem3  6071  enpw  6087  ce0nnuli  6178  fnfrec  6320

Copyright terms: Public domain

W3C validator