Theorem syl5eqner 2276

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

Hypotheses

Ref	Expression
syl5eqner.1	|- B = A
syl5eqner.2	|- ( ph -> B =/= C )

Assertion

Ref	Expression
syl5eqner	|- ( ph -> A =/= C )

Proof of Theorem syl5eqner

Step	Hyp	Ref	Expression
1		syl5eqner.2	. 2 |- ( ph -> B =/= C )
2		syl5eqner.1	. . 3 |- B = A
3	2	neeq1i 2260	. 2 |- ( B =/= C <-> A =/= C )
4	1, 3	sylib 120	1 |- ( ph -> A =/= C )

Syntax hints:   -> wi 4   = wceq 1284   =/= wne 2245

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-4 1440  ax-17 1459  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-ne 2246

This theorem is referenced by: (None)