Theorem wcon1 199

Description: Weak contraposition.

Hypothesis

Ref	Expression
wcon1.1	(a_|_ == b_|_) = 1

Assertion

Ref	Expression
wcon1	(a == b) = 1

Proof of Theorem wcon1

Step	Hyp	Ref	Expression
1		conb 114	. 2 (a == b) = (a_|_ == b_|_)
2		wcon1.1	. 2 (a_|_ == b_|_) = 1
3	1, 2	ax-r2 35	1 (a == b) = 1

Syntax hints:   = wb 1  _|_wn 4   == tb 5  1wt 9

This theorem is referenced by:  wcon3 201  wfh3 407  wfh4 408

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39

metamath.org