mt4 - Metamath Proof Explorer

	Metamath Proof Explorer		< Previous Next > Nearby theorems
Mirrors > Home > MPE Home > Th. List > mt4		Structured version Visualization version Unicode version

Theorem mt4 115

Description: The rule of modus tollens. Inference associated with con4i 113. (Contributed by Wolf Lammen, 12-May-2013.)

**Hypotheses**
Ref	Expression
mt4.1
mt4.2

**Assertion**
Ref	Expression
mt4

**Proof of Theorem mt4**
Step	Hyp	Ref	Expression
1		mt4.1	. 2
2		mt4.2	. . 3
3	2	con4i 113	. 2
4	1, 3	ax-mp 5	1

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

This theorem was proved from axioms: ax-mp 5 ax-3 8

This theorem is referenced by: infeq5i 8533 chirredi 29253