Theorem eqnetrrid 2378

Description: B chained equality inference for inequality. (Contributed by NM, 6-Jun-2012.)

Hypotheses

Ref	Expression
eqnetrrid.1	|- B = A
eqnetrrid.2	|- ( ph -> B =/= C )

Assertion

Ref	Expression
eqnetrrid	|- ( ph -> A =/= C )

Proof of Theorem eqnetrrid

Step	Hyp	Ref	Expression
1		eqnetrrid.2	. 2 |- ( ph -> B =/= C )
2		eqnetrrid.1	. . 3 |- B = A
3	2	neeq1i 2362	. 2 |- ( B =/= C <-> A =/= C )
4	1, 3	sylib 122	1 |- ( ph -> A =/= C )

Syntax hints:   -> wi 4   = wceq 1353   =/= wne 2347

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348

This theorem is referenced by: (None)