Theorem necomd 1640

Description: Deduction from commutative law for inequality.

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 1639	. 2 |- (A =/= B <-> B =/= A)
3	1, 2	sylib 198	1 |- (ph -> B =/= A)

Syntax hints:   -> wi 3   =/= wne 1588

This theorem is referenced by:  disjne 2319  ltnet 5528  xrltnet 5577  supxrbnd 6093  stadd 10168  strlem6 10178  hstrlem6 10186  efilcp 10556  efilcp2 10561  cnfilca 10562  dmse2 10595

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1472  df-ne 1590

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