Theorem neqcomd 2194

Description: Commute an inequality. (Contributed by Rohan Ridenour, 3-Aug-2023.)

Hypothesis

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

Assertion

Ref	Expression
neqcomd	|- ( ph -> -. B = A )

Proof of Theorem neqcomd

Step	Hyp	Ref	Expression
1		neqcomd.1	. 2 |- ( ph -> -. A = B )
2		eqcom 2191	. 2 |- ( A = B <-> B = A )
3	1, 2	sylnib 677	1 |- ( ph -> -. B = A )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1364

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 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-cleq 2182

This theorem is referenced by:  logbgcd1irraplemexp  14783