Theorem necomd 2331

Description: Deduction from commutative law for inequality. (Contributed by NM, 12-Feb-2008.)

Hypothesis

Ref	Expression
necomd.1	|- ( ph -> A =/= B )

Assertion

Ref	Expression
necomd	|- ( ph -> B =/= A )

Proof of Theorem necomd

Step	Hyp	Ref	Expression
1		necomd.1	. 2 |- ( ph -> A =/= B )
2		necom 2329	. 2 |- ( A =/= B <-> B =/= A )
3	1, 2	sylib 120	1 |- ( ph -> B =/= A )

Syntax hints:   -> wi 4   =/= 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-ext 2063

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

This theorem is referenced by:  difsnb  3528  0nelop  4003  fidifsnen  6355  ltned  7224  lt0ne0  7532  zdceq  8423  zneo  8448  xrlttri3  8872  qdceq  9256  flqltnz  9289  expival  9478  nn0opthd  9649  isprm2lem  10498